1 Context

1.1 Overall Factor Analysis Steps

  1. Are the data suitable for factor analysis?
    • Bartlett’s Sphericity Test Tests whether correlations are different than zero across all the data. If they are close to zero, there owuld be no common factors to find
    • Kaiser-Meyer-Olkin Criterion Test sampling adequacy, measures the degree to wich each variable predicts all other variables in the data set.
  2. Imputation of Missing Variables
    • Generate categorical values for missing data using Multiple Correspondence Analysis/Missing Fuzzy Average Method
  3. Calculate between-item Correlations
    • the polychoric (for orderd categorical variables) and regular Pearson correlation are calculated for later use in factor analysis and for checking other aspects of the factor analysis. The polychoric correlation is the input to the actual factor analysis.
  4. Estimate Number of Factors
    • Parallel analysis
    • Minimim Average Partial (MAP)
  5. Run factor analysis for a range of possible number of factors
    • produces
      • measures of model fit
      • communalities (how much each item covaries with the other items)
      • loadings (correlation between item and factor(s))
  6. Evaluate Reliability of Model..
    • alpha
    • omega
  7. Select best model (number of factors) given model fit statistics and judgement based on understanding of behavior.

1.2 Context Text Description

All data were used in the factorAnalysis1.1.html document you already received.

A series of factoro analyses were run on all items in the file factorAnalysis1.1.html. THe literature suggests doing this so you can compare both statistical measures of how well it fits, and also how logical the grouping of factors is according to knowledge of the subject.

This set of analyses showed that some items had really low communalities, meaning that they didn’t covary much with any of the other items. This means they will not be robust parts of any factor, and they recommend that you remove these from the analysis.

Models with different numbers of factors had different numbers of items with communalities less than 0.4. So a new data set was made for each number of factors, with only the items with communalities of 0.4 or larger.

Because each number of factors require a different data set (different numbers of items), all the steps had to be rerun sstarting with imputation. Those are the models included in this document.

2 Factor Analyses

Testing analyses from 11 - 18 factors.

2.1 11 Factors

2.1.1 Imputation of Missing Items (11 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.1.2 11-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.1.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.4178359^{4} with 2211 DF, p = 0e+00.

2.1.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8570731

2.1.3 11-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.1.3.1 Bartlett’s Test of Sphericity

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 5.8887983^{4} with 2211 DF, p = 0e+00.

2.1.3.2 11-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8570731

2.1.4 Between-Item Correlations

2.1.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.7175718. The maximum correlation in this data set is 0.8869939.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.6902268. The maximum correlation was 0.8853661.

2.1.5 Estimating Number of Factors

2.1.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

The suggested number of factors is 16.

2.1.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
Number of Factors MAP value
1 0.0252
2 0.0208
3 0.0163
4 0.0147
5 0.0142
6 0.0133
7 0.0126
8 0.0121
9 0.0118
10 0.0117
11 0.0115
12 0.0113
13 0.0114
14 0.0117
15 0.0117
16 0.0121
17 0.0121
18 0.0126

2.1.6 Factor Analysis for 11 Factors

2.1.6.1 11 Factors Model Fit

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

  • chi-square: 2.2247374^{4}
  • degrees of freedom: 1529
  • P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.4676849. Should be > 0.9; need reference)

2.1.6.2 11 Factor Model Communalities

fanal11.communality
TRAIN01 0.44
TRAIN02 0.24
TRAIN04 0.61
TRAIN05 0.32
TRAIN06 0.25
TRAIN07 0.60
TRAIN08 0.61
AGG09 0.76
AGG10 0.63
AGG11 0.76
AGG12 0.79
AGG13 0.95
AGG14 0.45
AGG15 0.76
AGG16 0.73
AGG17 0.55
AGG18 0.72
AGG19 0.59
AGG20 0.47
FEAR21 0.81
FEAR22 0.32
FEAR23 0.78
FEAR24 0.84
FEAR25 0.46
FEAR27 0.67
FEAR28 0.64
FEAR29 0.13
FEAR31 0.59
SEPR32 0.69
SEPR33 0.53
SEPR34 0.73
EXCITE35 0.48
EXCITE36 0.63
EXCITE37 0.58
EXCITE38 0.62
ATT39 0.29
ATT40 0.28
ATT41 0.32
ATT42 0.35
PLAY43 0.55
PLAY44 0.79
PLAY45 0.74
PLAY46 0.71
IMP47 0.46
IMP48 0.41
IMP49 0.39
MISC50 0.32
MISC51 0.37
MISC52 0.23
MISC54 0.58
MISC55 0.70
MISC56 0.53
MISC57 0.33
MISC58 0.23
MISC59 0.54
MISC60 0.38
MISC61 0.50
MISC62 0.48
MISC63 0.37
MISC64 0.54
MISC65 0.60
MISC66 0.69
MISC67 0.62
MISC68 0.20
MISC69 0.22
MISC70 0.33
MISC71 0.28

2.1.6.3 How many communalities < 0.40?

There are 21 items with communality < 0.40.

fanal11.communality item
TRAIN02 0.24 TRAIN02
TRAIN05 0.32 TRAIN05
TRAIN06 0.25 TRAIN06
FEAR22 0.32 FEAR22
FEAR29 0.13 FEAR29
ATT39 0.29 ATT39
ATT40 0.28 ATT40
ATT41 0.32 ATT41
ATT42 0.35 ATT42
IMP49 0.39 IMP49
MISC50 0.32 MISC50
MISC51 0.37 MISC51
MISC52 0.23 MISC52
MISC57 0.33 MISC57
MISC58 0.23 MISC58
MISC60 0.38 MISC60
MISC63 0.37 MISC63
MISC68 0.20 MISC68
MISC69 0.22 MISC69
MISC70 0.33 MISC70
MISC71 0.28 MISC71

2.1.6.4 11 Factor Model Loadings

PA2 PA10 PA1 PA5 PA11 PA6 PA8 PA3 PA4 PA7 PA9
TRAIN01 -0.14 -0.12 0.17 -0.02 -0.09 0.06 0.04 0.05 0.54 -0.02 -0.02
TRAIN02 -0.04 0.06 0.14 -0.02 0.00 0.03 0.01 -0.03 0.40 0.09 -0.06
TRAIN04 -0.04 0.05 0.30 0.01 -0.02 0.05 -0.04 -0.04 0.63 0.02 -0.08
TRAIN05 0.04 -0.15 0.12 0.14 -0.06 0.00 -0.02 0.13 0.43 0.07 0.02
TRAIN06 -0.09 0.02 0.21 -0.04 0.10 0.07 0.06 -0.12 0.30 -0.03 -0.13
TRAIN07 -0.13 0.02 0.60 -0.02 -0.03 0.05 0.03 -0.07 0.27 0.00 -0.06
TRAIN08 -0.74 0.01 0.08 0.01 0.06 0.01 -0.05 -0.03 0.06 0.05 0.03
AGG09 0.05 0.29 0.07 0.06 0.03 -0.06 0.08 0.71 0.03 -0.05 0.04
AGG10 0.03 0.05 -0.04 0.06 -0.03 0.06 0.19 0.68 -0.04 0.01 -0.01
AGG11 -0.09 -0.02 -0.13 0.81 0.00 0.12 0.04 0.01 0.09 -0.12 0.07
AGG12 -0.04 0.08 0.06 0.88 0.01 -0.03 -0.01 -0.04 -0.07 0.04 -0.03
AGG13 -0.01 0.03 0.02 0.95 0.01 -0.10 -0.02 0.07 0.03 0.05 0.01
AGG14 -0.09 0.05 -0.03 -0.07 0.05 0.08 0.16 0.59 -0.01 0.06 0.08
AGG15 -0.02 0.26 0.00 0.13 0.01 -0.03 0.06 0.70 0.01 -0.02 -0.04
AGG16 0.00 -0.04 0.09 0.02 0.02 -0.03 0.75 0.25 -0.01 0.00 -0.05
AGG17 0.10 0.08 -0.01 0.17 0.21 0.22 0.08 0.36 0.08 0.12 -0.35
AGG18 0.06 -0.08 0.05 0.03 -0.03 0.02 0.75 0.27 -0.02 -0.03 0.02
AGG19 0.15 -0.11 0.06 0.29 0.02 0.13 0.57 0.09 -0.06 0.10 -0.13
AGG20 0.02 -0.13 0.01 0.48 0.02 0.12 0.41 -0.07 -0.07 0.02 -0.04
FEAR21 0.01 0.83 0.03 0.07 0.02 0.06 -0.04 0.13 0.00 0.01 -0.04
FEAR22 -0.04 0.25 0.23 0.06 0.24 0.08 0.05 -0.21 -0.11 0.05 -0.04
FEAR23 0.00 0.79 0.01 0.00 0.06 0.05 0.01 0.18 -0.01 -0.01 0.02
FEAR24 -0.08 0.83 0.03 0.06 -0.01 0.00 0.00 0.15 -0.05 0.03 0.00
FEAR25 0.02 0.28 0.21 0.12 0.35 0.03 0.02 -0.08 0.05 0.02 0.06
FEAR27 -0.04 0.45 -0.10 -0.03 0.10 -0.04 0.59 -0.18 0.11 -0.03 0.10
FEAR28 0.07 0.49 0.20 0.06 0.38 0.06 -0.02 -0.09 -0.03 0.06 -0.09
FEAR29 -0.07 0.12 0.05 0.11 0.08 0.08 0.10 -0.04 0.08 0.08 -0.02
FEAR31 -0.07 0.42 -0.04 -0.04 0.12 -0.02 0.52 -0.29 0.11 -0.01 0.09
SEPR32 0.00 0.12 0.06 -0.02 -0.07 0.81 0.05 -0.04 -0.10 0.08 -0.06
SEPR33 -0.01 -0.01 0.08 0.05 -0.01 0.69 0.00 -0.08 -0.02 0.03 0.04
SEPR34 -0.03 -0.05 -0.07 -0.06 0.10 0.82 -0.04 0.06 0.12 -0.03 0.04
EXCITE35 -0.11 0.09 0.04 -0.11 -0.10 0.16 0.01 0.02 -0.05 0.64 0.06
EXCITE36 0.20 -0.01 0.05 0.00 0.02 -0.05 -0.08 0.03 -0.01 0.73 -0.04
EXCITE37 -0.07 -0.01 -0.04 0.02 -0.02 0.03 0.03 -0.01 0.04 0.77 -0.02
EXCITE38 0.03 -0.02 -0.14 0.05 0.09 -0.04 0.01 -0.05 0.06 0.76 0.00
ATT39 -0.06 0.09 0.14 -0.13 -0.11 0.08 0.03 0.09 -0.38 0.23 0.22
ATT40 -0.20 0.07 0.29 -0.03 0.08 0.13 0.03 0.05 -0.15 0.11 0.14
ATT41 -0.06 -0.02 0.13 0.08 -0.02 0.11 0.02 -0.07 -0.21 0.12 0.45
ATT42 -0.12 -0.02 0.08 0.02 0.07 0.13 0.10 -0.01 -0.04 0.16 0.43
PLAY43 0.52 -0.25 -0.02 -0.04 0.05 -0.09 0.00 -0.30 -0.02 0.06 0.12
PLAY44 0.88 0.00 0.03 -0.01 -0.01 0.00 0.08 -0.05 0.02 0.06 -0.02
PLAY45 0.82 0.06 -0.01 -0.10 -0.03 -0.06 0.02 0.00 -0.05 0.01 0.06
PLAY46 0.77 -0.04 -0.14 -0.01 0.03 0.05 -0.06 0.10 0.07 0.04 -0.08
IMP47 0.21 0.09 -0.06 0.02 -0.01 0.04 0.05 0.00 0.43 0.17 0.29
IMP48 0.15 0.04 0.04 0.20 0.00 0.05 0.05 -0.05 0.28 0.13 0.32
IMP49 0.00 0.05 0.05 0.20 -0.02 -0.05 0.01 0.00 0.45 0.16 0.16
MISC50 0.04 0.00 -0.03 0.20 0.09 0.24 -0.06 0.02 0.20 0.08 0.21
MISC51 -0.13 -0.16 -0.01 0.02 0.02 0.28 0.01 0.11 0.35 0.05 0.17
MISC52 -0.32 -0.04 0.00 0.06 0.05 -0.07 0.05 0.00 0.05 0.11 0.34
MISC54 -0.11 0.02 0.16 0.00 0.66 -0.02 0.02 -0.04 0.00 0.08 -0.02
MISC55 0.02 -0.03 -0.04 -0.06 0.87 0.02 0.01 0.04 -0.07 0.00 0.00
MISC56 -0.03 -0.03 0.03 0.11 0.70 -0.03 -0.04 0.01 0.01 -0.04 0.03
MISC57 0.06 -0.06 0.10 0.14 -0.05 0.16 -0.01 -0.05 0.24 0.10 0.26
MISC58 0.13 -0.03 0.06 0.33 0.00 0.26 -0.04 0.00 0.04 -0.12 0.11
MISC59 0.27 0.05 0.14 0.10 -0.02 0.37 -0.08 -0.04 0.13 -0.02 0.37
MISC60 0.30 0.02 0.07 -0.04 -0.03 0.06 -0.14 0.01 -0.01 0.14 0.41
MISC61 0.43 0.01 0.04 -0.01 -0.12 0.17 -0.13 0.11 -0.06 0.16 0.30
MISC62 0.00 -0.03 0.40 -0.04 -0.01 -0.06 0.41 0.04 0.09 0.04 0.22
MISC63 -0.01 -0.02 0.35 0.04 0.11 -0.14 0.08 0.05 0.09 0.14 0.31
MISC64 -0.07 -0.14 0.66 0.00 0.06 0.05 0.02 0.07 0.08 -0.04 0.00
MISC65 -0.09 -0.12 0.62 -0.04 0.05 0.05 0.14 0.04 0.15 -0.04 0.09
MISC66 -0.05 0.21 0.63 -0.01 0.18 0.05 -0.06 0.00 0.07 -0.06 0.02
MISC67 -0.07 0.20 0.63 0.07 0.11 0.07 -0.01 -0.04 -0.06 -0.06 0.05
MISC68 0.02 -0.13 -0.09 0.10 0.31 0.07 0.00 0.12 0.19 0.05 0.08
MISC69 -0.07 -0.05 -0.07 -0.01 0.33 0.10 0.03 0.11 0.14 0.03 0.20
MISC70 0.02 -0.06 -0.05 0.07 0.08 0.14 0.08 0.19 0.08 0.00 0.43
MISC71 -0.03 -0.04 0.08 -0.05 0.26 0.10 -0.07 0.08 0.05 -0.06 0.38
2.1.6.4.1 11 Factor Model Largest Loading Per Item
Largest Loading Per Item and Associated Factors, Sorted by Factor
largest maximum itemNames itemDescriptions
14 PA1 0.29 ATT40 Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
45 PA1 0.35 MISC63 Becomes highly excited and/or distracted when encountering unfamiliar people
46 PA1 0.66 MISC64 When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
47 PA1 0.62 MISC65 Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
48 PA1 0.63 MISC66 Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
49 PA1 0.63 MISC67 Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
66 PA1 0.60 TRAIN07 Unfocused; is easily distracted by interesting sights, sounds or smells
67 PA1 0.08 TRAIN08 Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
21 PA10 0.83 FEAR21 When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
22 PA10 0.25 FEAR22 In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
23 PA10 0.79 FEAR23 When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
24 PA10 0.83 FEAR24 When an unfamiliar person tries to touch or pet the dog
27 PA10 0.49 FEAR28 When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
28 PA10 0.12 FEAR29 When having nails trimmed, or feet touched/handled
25 PA11 0.35 FEAR25 In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
36 PA11 0.66 MISC54 Reluctant to/nervous about crossing grates or other unfamiliar surfaces
37 PA11 0.87 MISC55 Reluctant to/nervous about crossing shiny or slippery floors
38 PA11 0.70 MISC56 Nervous or frightened when ascending or descending some types of stairs
50 PA11 0.31 MISC68 Chases own tail/hind end
51 PA11 0.33 MISC69 Chases/follows shadows, light spots, etc.
43 PA2 0.43 MISC61 Active, energetic, always on the go
54 PA2 0.52 PLAY43 Eagerly engages in play with new/unfamiliar people
55 PA2 0.88 PLAY44 Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
56 PA2 0.82 PLAY45 Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
57 PA2 0.77 PLAY46 Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1 PA3 0.71 AGG09 Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2 PA3 0.68 AGG10 Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6 PA3 0.59 AGG14 When strangers walk past when the dog is in his/her home run or kennel
7 PA3 0.70 AGG15 When an unfamiliar person tries to touch or pet the dog
9 PA3 0.36 AGG17 When stared at directly by you or another familiar person
30 PA4 0.43 IMP47 Impulsive; doesn’t seem to think before s/he acts
32 PA4 0.45 IMP49 Is difficult to interrupt or distract when doing things s/he wants to do
34 PA4 0.35 MISC51 Escapes or would escape from home, yard or kennel given the chance
61 PA4 0.54 TRAIN01 Is hard to recall when off the leash
62 PA4 0.40 TRAIN02 Is slow to obey a ‘sit’ command
63 PA4 0.63 TRAIN04 Has difficulty attending/listening to things you say or do
64 PA4 0.43 TRAIN05 Is slow to respond to corrections or reprimands: thick-skinned
65 PA4 0.30 TRAIN06 Is slow to learn new tricks or tasks
3 PA5 0.81 AGG11 Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4 PA5 0.88 AGG12 When you or another familiar person approaches the dog directly while s/he is eating
5 PA5 0.95 AGG13 When his/her food is taken away by you or another familiar person
12 PA5 0.48 AGG20 When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
40 PA5 0.33 MISC58 Urinates against objects/furnishings indoors
33 PA6 0.24 MISC50 NA
41 PA6 0.37 MISC59 Hyperactive, restless, has trouble settling down
58 PA6 0.81 SEPR32 Restlessness/agitation/pacing when left alone
59 PA6 0.69 SEPR33 Barking or whining when left alone
60 PA6 0.82 SEPR34 Chewing/scratching at doors, floor, fencing, etc., when left alone
13 PA7 0.23 ATT39 Displays a strong attachment for you or another familiar person
17 PA7 0.64 EXCITE35 Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
18 PA7 0.73 EXCITE36 Excitable when playing with you or other familiar persons
19 PA7 0.77 EXCITE37 Excitable just before being taken out for a walk
20 PA7 0.76 EXCITE38 Excitable just before being taken out for work or training
8 PA8 0.75 AGG16 When approached directly by an unfamiliar dog while being walked/exercised on a leash
10 PA8 0.75 AGG18 When barked, growled, or lunged at by another dog
11 PA8 0.57 AGG19 Towards other familiar dogs
26 PA8 0.59 FEAR27 When approached directly by an unfamiliar dog
29 PA8 0.52 FEAR31 When barked, growled, or lunged at by an unfamiliar dog
44 PA8 0.41 MISC62 Becomes highly excited and/or distracted when encountering unfamiliar dogs
15 PA9 0.45 ATT41 Tends to nudge or paw you (or others) for attention
16 PA9 0.43 ATT42 Becomes agitated (whines, jumps up, tries to intervene) when attention is given to another person or animal
31 PA9 0.32 IMP48 Becomes frustrated/impatient in a wide range of situations
35 PA9 0.34 MISC52 Begs persistently for food when people are eating
39 PA9 0.26 MISC57 Pulls excessively hard when on leash
42 PA9 0.41 MISC60 Playful, puppyish, boisterous
52 PA9 0.43 MISC70 Barks persistently when alarmed or excited
53 PA9 0.38 MISC71 Licks people or objects excessively

2.1.7 11 Model Reliability Measures

The overall alpha for all items is 0.8806686.

The overall omega for all items is 0.921832.

Hierarchical omega is 0.5481117.

2.2 12 Factors

2.2.1 Imputation of Missing Items (12 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.2.2 12-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.2.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.5696263^{4} with 2278 DF, p = 0e+00.

2.2.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8570906

2.2.3 12-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.2.3.1 Bartlett’s Test of Sphericity

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.0101668^{4} with 2278 DF, p = 0e+00.

2.2.3.2 12-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8570906

2.2.4 Between-Item Correlations

2.2.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.7175318. The maximum correlation in this data set is 0.8879515.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.6908209. The maximum correlation was 0.8870493.

2.2.5 Estimating Number of Factors

2.2.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

The suggested number of factors is 16.

2.2.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
Number of Factors MAP value
1 0.0252
2 0.0210
3 0.0162
4 0.0145
5 0.0139
6 0.0131
7 0.0125
8 0.0121
9 0.0116
10 0.0115
11 0.0109
12 0.0110
13 0.0113
14 0.0114
15 0.0115
16 0.0118
17 0.0122
18 0.0124

2.2.6 Factor Analysis for 12 Factors

2.2.6.1 12 Factors Model Fit

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

  • chi-square: 2.2047631^{4}
  • degrees of freedom: 1528
  • P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.4668955. Should be > 0.9; need reference)

2.2.6.2 12 Factor Model Communalities

fanal12.communality
TRAIN01 0.46
TRAIN02 0.32
TRAIN03 0.41
TRAIN04 0.62
TRAIN05 0.33
TRAIN06 0.27
TRAIN07 0.61
TRAIN08 0.61
AGG09 0.75
AGG10 0.66
AGG11 0.76
AGG12 0.78
AGG13 0.96
AGG14 0.49
AGG15 0.78
AGG16 0.75
AGG17 0.58
AGG18 0.74
AGG19 0.61
AGG20 0.46
FEAR21 0.81
FEAR22 0.31
FEAR23 0.80
FEAR24 0.84
FEAR25 0.46
FEAR27 0.66
FEAR28 0.64
FEAR29 0.16
FEAR31 0.58
SEPR32 0.67
SEPR33 0.53
SEPR34 0.70
EXCITE35 0.50
EXCITE36 0.63
EXCITE37 0.57
EXCITE38 0.61
ATT39 0.29
ATT40 0.34
ATT41 0.31
ATT42 0.34
PLAY43 0.55
PLAY44 0.81
PLAY45 0.76
PLAY46 0.72
IMP47 0.47
IMP48 0.42
IMP49 0.39
MISC50 0.30
MISC51 0.35
MISC52 0.43
MISC53 0.44
MISC54 0.62
MISC55 0.73
MISC56 0.57
MISC57 0.35
MISC58 0.25
MISC59 0.55
MISC60 0.50
MISC61 0.67
MISC62 0.51
MISC63 0.38
MISC64 0.57
MISC65 0.61
MISC66 0.68
MISC67 0.60
MISC69 0.15
MISC70 0.33
MISC71 0.26

2.2.6.3 How many communalities < 0.40?

There are 18 items with communality < 0.40.

fanal12.communality item
TRAIN02 0.32 TRAIN02
TRAIN05 0.33 TRAIN05
TRAIN06 0.27 TRAIN06
FEAR22 0.31 FEAR22
FEAR29 0.16 FEAR29
ATT39 0.29 ATT39
ATT40 0.34 ATT40
ATT41 0.31 ATT41
ATT42 0.34 ATT42
IMP49 0.39 IMP49
MISC50 0.30 MISC50
MISC51 0.35 MISC51
MISC57 0.35 MISC57
MISC58 0.25 MISC58
MISC63 0.38 MISC63
MISC69 0.15 MISC69
MISC70 0.33 MISC70
MISC71 0.26 MISC71

2.2.6.4 12 Factor Model Loadings

PA10 PA1 PA2 PA5 PA4 PA6 PA8 PA11 PA3 PA9 PA7 PA12
TRAIN01 -0.12 0.11 -0.10 -0.02 0.57 0.05 0.03 -0.06 0.06 -0.05 0.07 -0.02
TRAIN02 0.07 0.02 -0.04 -0.08 0.54 0.02 0.01 0.05 0.00 0.10 0.01 -0.05
TRAIN03 -0.01 -0.01 -0.10 -0.10 0.58 0.11 0.03 0.04 -0.01 0.11 0.01 0.03
TRAIN04 0.07 0.23 -0.03 0.01 0.67 0.03 -0.03 -0.02 -0.05 0.00 -0.05 -0.01
TRAIN05 -0.15 0.07 0.03 0.14 0.45 -0.02 0.02 -0.04 0.12 0.06 0.01 0.08
TRAIN06 0.02 0.16 -0.06 -0.05 0.36 0.07 0.04 0.10 -0.11 -0.02 -0.05 -0.14
TRAIN07 0.04 0.59 -0.12 0.00 0.30 0.04 0.03 -0.05 -0.09 0.00 -0.06 -0.03
TRAIN08 0.03 0.09 -0.71 0.00 0.07 0.01 -0.04 0.07 -0.03 0.05 0.06 -0.03
AGG09 0.29 0.08 0.06 0.06 0.03 -0.06 0.12 0.02 0.67 -0.06 -0.01 0.06
AGG10 0.03 -0.02 0.08 0.04 -0.04 0.08 0.18 -0.05 0.70 0.00 0.05 -0.08
AGG11 -0.01 -0.13 -0.10 0.80 0.07 0.12 0.06 0.00 0.00 -0.12 0.05 0.06
AGG12 0.08 0.04 -0.06 0.88 -0.06 -0.02 0.00 0.01 -0.04 0.05 -0.03 -0.01
AGG13 0.03 0.06 0.02 0.96 0.00 -0.09 -0.02 -0.02 0.07 0.05 0.04 -0.03
AGG14 0.04 0.04 0.01 -0.07 -0.05 0.11 0.13 0.01 0.61 0.03 0.17 -0.08
AGG15 0.26 -0.05 -0.07 0.12 0.04 -0.06 0.11 0.05 0.70 -0.02 -0.05 0.08
AGG16 -0.01 0.05 -0.04 0.00 0.02 -0.04 0.79 0.04 0.19 0.00 -0.06 -0.01
AGG17 0.04 0.09 0.21 0.23 0.03 0.24 0.04 0.14 0.38 0.10 -0.19 -0.32
AGG18 -0.06 0.02 0.02 0.01 0.00 0.02 0.78 -0.01 0.22 -0.03 0.00 0.02
AGG19 -0.09 -0.02 0.05 0.27 -0.01 0.11 0.63 0.04 0.04 0.12 -0.16 0.02
AGG20 -0.12 -0.02 0.04 0.45 -0.05 0.13 0.40 0.03 -0.06 0.02 0.04 -0.11
FEAR21 0.83 0.00 -0.01 0.08 0.01 0.05 -0.05 0.03 0.13 0.01 -0.04 0.00
FEAR22 0.24 0.17 -0.06 0.03 -0.04 0.08 0.02 0.27 -0.18 0.07 0.00 -0.06
FEAR23 0.81 0.01 -0.02 0.01 0.00 0.05 0.01 0.05 0.16 -0.01 -0.04 0.05
FEAR24 0.85 0.01 -0.10 0.07 -0.04 0.00 -0.01 -0.01 0.12 0.03 -0.01 0.02
FEAR25 0.29 0.24 0.07 0.13 0.05 0.05 -0.02 0.31 -0.08 0.01 0.07 -0.05
FEAR27 0.47 -0.03 0.04 -0.01 0.03 -0.03 0.53 0.06 -0.21 -0.04 0.20 -0.11
FEAR28 0.47 0.16 0.07 0.05 0.01 0.07 -0.05 0.40 -0.06 0.07 -0.06 -0.09
FEAR29 0.11 0.07 0.02 0.09 0.08 0.10 0.04 0.06 0.01 0.07 0.13 -0.18
FEAR31 0.42 0.01 0.03 -0.04 0.05 0.01 0.43 0.09 -0.28 -0.03 0.23 -0.16
SEPR32 0.11 0.03 -0.02 -0.03 -0.06 0.80 0.04 -0.06 -0.02 0.09 -0.08 -0.01
SEPR33 -0.01 0.05 -0.03 0.03 0.02 0.69 0.00 0.00 -0.07 0.03 0.02 0.04
SEPR34 -0.05 -0.03 -0.01 -0.04 0.08 0.81 -0.05 0.07 0.06 -0.05 0.05 0.03
EXCITE35 0.10 0.01 -0.15 -0.12 -0.01 0.14 0.05 -0.09 0.00 0.64 0.01 0.11
EXCITE36 -0.02 0.05 0.17 0.02 0.00 -0.06 -0.06 0.02 0.02 0.72 -0.05 0.05
EXCITE37 -0.02 -0.05 -0.07 0.03 0.04 0.03 0.04 -0.01 -0.01 0.75 0.02 0.02
EXCITE38 -0.03 -0.13 0.06 0.06 0.05 -0.03 0.00 0.09 -0.05 0.74 0.05 -0.02
ATT39 0.10 0.20 -0.01 -0.15 -0.36 0.12 0.00 -0.14 0.10 0.23 0.17 0.02
ATT40 0.06 0.41 -0.06 -0.02 -0.18 0.18 -0.04 0.00 0.08 0.10 0.20 -0.15
ATT41 0.00 0.22 0.03 0.05 -0.23 0.16 -0.01 -0.06 -0.06 0.10 0.37 0.10
ATT42 0.01 0.18 -0.04 0.01 -0.09 0.17 0.08 0.02 -0.03 0.13 0.35 0.14
PLAY43 -0.24 -0.01 0.49 -0.03 -0.05 -0.09 -0.01 0.03 -0.30 0.06 0.06 0.11
PLAY44 -0.01 0.03 0.87 -0.01 0.02 0.01 0.06 -0.03 -0.04 0.06 -0.05 0.03
PLAY45 0.03 0.00 0.83 -0.09 -0.08 -0.05 -0.02 -0.05 0.03 0.01 0.05 0.05
PLAY46 -0.07 -0.15 0.76 0.00 0.05 0.04 -0.08 0.02 0.12 0.03 -0.06 0.01
IMP47 0.09 -0.05 0.30 0.01 0.38 0.06 0.01 -0.01 0.03 0.12 0.33 0.09
IMP48 0.04 0.05 0.23 0.17 0.24 0.07 0.01 0.01 -0.01 0.10 0.34 0.09
IMP49 0.04 0.09 0.11 0.20 0.40 -0.04 -0.02 -0.05 0.02 0.13 0.24 -0.03
MISC50 0.01 0.05 0.09 0.22 0.13 0.26 -0.05 0.05 -0.01 0.05 0.14 0.12
MISC51 -0.15 0.02 -0.09 0.04 0.28 0.27 0.01 0.00 0.11 0.01 0.20 0.10
MISC52 -0.07 0.02 -0.18 0.03 0.00 -0.05 -0.06 0.06 0.12 0.07 0.61 -0.06
MISC53 -0.13 -0.08 -0.15 0.19 0.15 0.04 -0.09 -0.01 0.02 0.02 0.54 0.01
MISC54 -0.01 0.16 -0.04 -0.01 0.01 -0.01 -0.02 0.69 0.00 0.07 0.09 -0.14
MISC55 -0.02 -0.07 -0.02 -0.08 -0.04 0.02 0.04 0.89 0.02 0.01 -0.04 0.04
MISC56 -0.03 -0.01 -0.06 0.10 0.02 -0.04 -0.01 0.74 0.01 -0.04 0.00 0.06
MISC57 -0.04 0.05 0.00 0.13 0.25 0.14 0.03 0.00 -0.06 0.09 0.15 0.27
MISC58 -0.04 -0.01 0.05 0.32 0.06 0.24 0.00 0.06 -0.01 -0.11 0.00 0.20
MISC59 0.06 0.11 0.18 0.09 0.11 0.35 -0.02 0.03 -0.06 -0.02 0.15 0.40
MISC60 0.06 0.03 0.11 -0.05 -0.01 0.01 -0.02 0.03 -0.06 0.14 0.04 0.60
MISC61 0.04 -0.02 0.19 -0.02 -0.05 0.12 0.01 -0.04 0.03 0.18 -0.10 0.64
MISC62 -0.01 0.39 -0.06 -0.04 0.07 -0.09 0.46 0.02 -0.02 0.03 0.09 0.22
MISC63 -0.01 0.38 -0.02 0.04 0.06 -0.14 0.10 0.12 0.03 0.12 0.20 0.22
MISC64 -0.15 0.72 -0.05 0.04 0.06 0.05 0.02 0.01 0.06 -0.05 -0.03 -0.01
MISC65 -0.11 0.65 -0.06 -0.01 0.15 0.04 0.13 0.03 0.02 -0.06 0.07 0.02
MISC66 0.20 0.61 -0.05 -0.01 0.10 0.04 -0.08 0.18 0.01 -0.06 0.01 0.00
MISC67 0.19 0.58 -0.10 0.06 -0.01 0.07 -0.01 0.14 -0.02 -0.05 0.00 0.03
MISC69 0.00 0.06 -0.01 0.03 0.04 0.12 0.04 0.21 0.04 0.00 0.13 0.08
MISC70 -0.05 -0.02 0.02 0.05 0.03 0.15 0.10 0.12 0.18 -0.02 0.31 0.27
MISC71 -0.01 0.19 0.04 -0.04 -0.02 0.13 -0.07 0.20 0.05 -0.09 0.28 0.15
2.2.6.4.1 12 Factor Model Largest Loading Per Item
Largest Loading Per Item and Associated Factors, Sorted by Factor
largest maximum itemNames itemDescriptions
14 PA1 0.41 ATT40 Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
46 PA1 0.38 MISC63 Becomes highly excited and/or distracted when encountering unfamiliar people
47 PA1 0.72 MISC64 When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
48 PA1 0.65 MISC65 Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
49 PA1 0.61 MISC66 Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
50 PA1 0.58 MISC67 Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
67 PA1 0.59 TRAIN07 Unfocused; is easily distracted by interesting sights, sounds or smells
68 PA1 0.09 TRAIN08 Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
21 PA10 0.83 FEAR21 When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
23 PA10 0.81 FEAR23 When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
24 PA10 0.85 FEAR24 When an unfamiliar person tries to touch or pet the dog
27 PA10 0.47 FEAR28 When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
22 PA11 0.27 FEAR22 In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
25 PA11 0.31 FEAR25 In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
37 PA11 0.69 MISC54 Reluctant to/nervous about crossing grates or other unfamiliar surfaces
38 PA11 0.89 MISC55 Reluctant to/nervous about crossing shiny or slippery floors
39 PA11 0.74 MISC56 Nervous or frightened when ascending or descending some types of stairs
51 PA11 0.21 MISC69 Chases/follows shadows, light spots, etc.
40 PA12 0.27 MISC57 Pulls excessively hard when on leash
42 PA12 0.40 MISC59 Hyperactive, restless, has trouble settling down
43 PA12 0.60 MISC60 Playful, puppyish, boisterous
44 PA12 0.64 MISC61 Active, energetic, always on the go
54 PA2 0.49 PLAY43 Eagerly engages in play with new/unfamiliar people
55 PA2 0.87 PLAY44 Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
56 PA2 0.83 PLAY45 Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
57 PA2 0.76 PLAY46 Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1 PA3 0.67 AGG09 Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2 PA3 0.70 AGG10 Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6 PA3 0.61 AGG14 When strangers walk past when the dog is in his/her home run or kennel
7 PA3 0.70 AGG15 When an unfamiliar person tries to touch or pet the dog
9 PA3 0.38 AGG17 When stared at directly by you or another familiar person
30 PA4 0.38 IMP47 Impulsive; doesn’t seem to think before s/he acts
32 PA4 0.40 IMP49 Is difficult to interrupt or distract when doing things s/he wants to do
34 PA4 0.28 MISC51 Escapes or would escape from home, yard or kennel given the chance
61 PA4 0.57 TRAIN01 Is hard to recall when off the leash
62 PA4 0.54 TRAIN02 Is slow to obey a ‘sit’ command
63 PA4 0.58 TRAIN03 Is slow to obey a ‘stay’ command
64 PA4 0.67 TRAIN04 Has difficulty attending/listening to things you say or do
65 PA4 0.45 TRAIN05 Is slow to respond to corrections or reprimands: thick-skinned
66 PA4 0.36 TRAIN06 Is slow to learn new tricks or tasks
3 PA5 0.80 AGG11 Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4 PA5 0.88 AGG12 When you or another familiar person approaches the dog directly while s/he is eating
5 PA5 0.96 AGG13 When his/her food is taken away by you or another familiar person
12 PA5 0.45 AGG20 When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
41 PA5 0.32 MISC58 Urinates against objects/furnishings indoors
33 PA6 0.26 MISC50 NA
58 PA6 0.80 SEPR32 Restlessness/agitation/pacing when left alone
59 PA6 0.69 SEPR33 Barking or whining when left alone
60 PA6 0.81 SEPR34 Chewing/scratching at doors, floor, fencing, etc., when left alone
15 PA7 0.37 ATT41 Tends to nudge or paw you (or others) for attention
16 PA7 0.35 ATT42 Becomes agitated (whines, jumps up, tries to intervene) when attention is given to another person or animal
28 PA7 0.13 FEAR29 When having nails trimmed, or feet touched/handled
31 PA7 0.34 IMP48 Becomes frustrated/impatient in a wide range of situations
35 PA7 0.61 MISC52 Begs persistently for food when people are eating
36 PA7 0.54 MISC53 Steals food
52 PA7 0.31 MISC70 Barks persistently when alarmed or excited
53 PA7 0.28 MISC71 Licks people or objects excessively
8 PA8 0.79 AGG16 When approached directly by an unfamiliar dog while being walked/exercised on a leash
10 PA8 0.78 AGG18 When barked, growled, or lunged at by another dog
11 PA8 0.63 AGG19 Towards other familiar dogs
26 PA8 0.53 FEAR27 When approached directly by an unfamiliar dog
29 PA8 0.43 FEAR31 When barked, growled, or lunged at by an unfamiliar dog
45 PA8 0.46 MISC62 Becomes highly excited and/or distracted when encountering unfamiliar dogs
13 PA9 0.23 ATT39 Displays a strong attachment for you or another familiar person
17 PA9 0.64 EXCITE35 Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
18 PA9 0.72 EXCITE36 Excitable when playing with you or other familiar persons
19 PA9 0.75 EXCITE37 Excitable just before being taken out for a walk
20 PA9 0.74 EXCITE38 Excitable just before being taken out for work or training

2.2.7 12 Model Reliability Measures

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

The overall alpha for all items is 0.884123.

The overall omega for all items is 0.9258431.

Hierarchical omega is 0.5616952.

2.3 13 Factors

2.3.1 Imputation of Missing Items (13 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.3.2 13-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.3.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.7613184^{4} with 2415 DF, p = 0e+00.

2.3.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8576926

2.3.3 13-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.3.3.1 Bartlett’s Test of Sphericity

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.1941027^{4} with 2415 DF, p = 0e+00.

2.3.3.2 13-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8576926

2.3.4 Between-Item Correlations

2.3.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.717518. The maximum correlation in this data set is 0.8872086.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.6908064. The maximum correlation was 0.8850145.

2.3.5 Estimating Number of Factors

2.3.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

The suggested number of factors is 16.

2.3.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
Number of Factors MAP value
1 0.0244
2 0.0205
3 0.0158
4 0.0142
5 0.0135
6 0.0127
7 0.0121
8 0.0118
9 0.0115
10 0.0114
11 0.0111
12 0.0107
13 0.0109
14 0.0111
15 0.0113
16 0.0115
17 0.0118
18 0.0119

2.3.6 Factor Analysis for 13 Factors

2.3.6.1 13 Factors Model Fit

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

  • chi-square: 2.2297571^{4}
  • degrees of freedom: 1583
  • P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.4646876. Should be > 0.9; need reference)

2.3.6.2 13 Factor Model Communalities

fanal13.communality
TRAIN01 0.46
TRAIN02 0.38
TRAIN03 0.50
TRAIN04 0.62
TRAIN05 0.34
TRAIN06 0.27
TRAIN07 0.61
TRAIN08 0.60
AGG09 0.74
AGG10 0.65
AGG11 0.75
AGG12 0.79
AGG13 0.95
AGG14 0.48
AGG15 0.77
AGG16 0.77
AGG17 0.79
AGG18 0.73
AGG19 0.62
AGG20 0.48
FEAR21 0.80
FEAR22 0.32
FEAR23 0.80
FEAR24 0.86
FEAR25 0.45
FEAR26 0.44
FEAR27 0.74
FEAR28 0.66
FEAR29 0.46
FEAR30 0.56
FEAR31 0.63
SEPR32 0.67
SEPR33 0.54
SEPR34 0.73
EXCITE35 0.50
EXCITE36 0.62
EXCITE37 0.59
EXCITE38 0.63
ATT39 0.29
ATT40 0.30
ATT41 0.30
ATT42 0.33
PLAY43 0.55
PLAY44 0.79
PLAY45 0.75
PLAY46 0.70
IMP47 0.45
IMP48 0.42
IMP49 0.39
MISC50 0.34
MISC51 0.39
MISC52 0.44
MISC53 0.45
MISC54 0.62
MISC55 0.75
MISC56 0.54
MISC57 0.34
MISC58 0.25
MISC59 0.55
MISC60 0.40
MISC61 0.54
MISC62 0.48
MISC63 0.38
MISC64 0.59
MISC65 0.63
MISC66 0.67
MISC67 0.59
MISC69 0.24
MISC70 0.34
MISC71 0.28

2.3.6.3 How many communalities < 0.40?

There are 18 items with communality < 0.40.

fanal13.communality item
TRAIN02 0.38 TRAIN02
TRAIN05 0.34 TRAIN05
TRAIN06 0.27 TRAIN06
FEAR22 0.32 FEAR22
ATT39 0.29 ATT39
ATT40 0.30 ATT40
ATT41 0.30 ATT41
ATT42 0.33 ATT42
IMP49 0.39 IMP49
MISC50 0.34 MISC50
MISC51 0.39 MISC51
MISC57 0.34 MISC57
MISC58 0.25 MISC58
MISC60 0.40 MISC60
MISC63 0.38 MISC63
MISC69 0.24 MISC69
MISC70 0.34 MISC70
MISC71 0.28 MISC71

2.3.6.4 13 Factor Model Loadings

PA12 PA2 PA1 PA4 PA6 PA13 PA8 PA5 PA9 PA3 PA11 PA10 PA7
TRAIN01 -0.13 -0.09 0.16 -0.02 0.04 0.53 0.00 -0.10 -0.05 0.05 0.14 0.05 -0.11
TRAIN02 0.05 -0.04 -0.03 -0.08 -0.01 0.59 0.03 0.07 0.06 0.03 -0.08 0.13 0.07
TRAIN03 -0.03 -0.07 -0.05 -0.09 0.10 0.66 0.06 0.06 0.07 0.03 -0.09 0.10 0.15
TRAIN04 0.08 -0.04 0.24 0.03 0.02 0.65 -0.02 -0.01 0.00 -0.07 0.00 -0.06 -0.07
TRAIN05 -0.12 0.04 0.09 0.17 -0.02 0.45 0.04 -0.02 0.06 0.10 0.05 -0.13 0.00
TRAIN06 0.02 -0.11 0.12 -0.05 0.04 0.37 0.07 0.14 -0.04 -0.12 -0.08 0.02 -0.04
TRAIN07 0.04 -0.13 0.60 -0.01 0.02 0.28 0.02 -0.05 -0.01 -0.10 -0.08 0.03 -0.03
TRAIN08 0.04 -0.71 0.11 0.01 0.01 0.07 -0.06 0.05 0.04 -0.03 0.06 0.02 0.00
AGG09 0.33 0.07 0.09 0.07 -0.05 0.03 0.16 0.03 -0.06 0.62 0.02 -0.05 -0.08
AGG10 0.06 0.05 -0.05 0.02 0.06 -0.03 0.24 -0.04 -0.01 0.66 0.02 0.07 -0.10
AGG11 0.00 -0.08 -0.10 0.80 0.14 0.05 0.05 -0.03 -0.11 -0.01 0.10 0.02 -0.04
AGG12 0.08 -0.09 0.02 0.87 -0.04 -0.04 0.04 0.04 0.06 -0.04 -0.08 -0.03 0.02
AGG13 0.03 0.01 0.05 0.94 -0.10 -0.01 -0.01 -0.02 0.05 0.07 0.01 0.08 -0.04
AGG14 0.07 -0.06 0.03 -0.07 0.09 -0.06 0.18 0.02 0.05 0.56 0.15 0.00 -0.09
AGG15 0.30 -0.01 -0.04 0.12 -0.04 0.05 0.14 0.03 -0.05 0.66 -0.03 0.03 -0.05
AGG16 0.00 -0.04 0.05 0.00 -0.05 0.04 0.82 0.06 0.00 0.16 -0.04 -0.03 0.00
AGG17 0.04 0.12 0.12 0.17 0.20 -0.07 0.01 0.08 0.13 0.26 -0.02 0.08 -0.65
AGG18 -0.05 0.04 0.04 0.02 0.02 0.01 0.79 -0.01 -0.03 0.19 0.03 0.00 0.00
AGG19 -0.09 0.09 -0.02 0.27 0.11 0.01 0.64 0.04 0.09 0.04 -0.15 0.05 -0.01
AGG20 -0.16 0.00 -0.05 0.44 0.09 -0.03 0.43 0.05 0.00 -0.04 -0.06 0.15 0.06
FEAR21 0.82 -0.01 0.00 0.08 0.04 0.01 -0.06 0.04 0.01 0.10 -0.02 0.06 -0.03
FEAR22 0.20 -0.08 0.13 0.02 0.05 -0.01 0.03 0.30 0.05 -0.14 -0.11 0.13 0.10
FEAR23 0.82 -0.02 0.01 0.01 0.05 0.00 0.02 0.07 0.00 0.13 -0.01 -0.04 0.00
FEAR24 0.86 -0.10 0.00 0.06 -0.01 -0.03 -0.02 -0.01 0.04 0.11 -0.01 0.05 0.02
FEAR25 0.29 0.02 0.23 0.12 0.03 0.04 -0.01 0.33 0.03 -0.10 0.05 0.01 -0.01
FEAR26 0.36 0.08 0.00 0.09 0.08 0.04 0.00 -0.01 -0.02 0.04 -0.01 0.43 0.01
FEAR27 0.46 -0.01 0.01 -0.03 -0.05 -0.03 0.48 0.02 -0.01 -0.28 0.32 0.08 -0.13
FEAR28 0.46 0.06 0.13 0.03 0.03 0.02 -0.06 0.40 0.04 -0.07 -0.10 0.18 -0.04
FEAR29 0.00 0.05 0.04 0.03 0.06 0.07 -0.03 -0.01 0.00 0.05 0.03 0.65 -0.05
FEAR30 -0.01 0.09 0.06 0.13 0.12 0.03 0.01 0.13 -0.05 -0.03 0.00 0.62 -0.03
FEAR31 0.37 -0.03 0.03 -0.08 -0.02 -0.01 0.37 0.06 0.00 -0.33 0.30 0.17 -0.11
SEPR32 0.10 -0.04 0.01 -0.05 0.79 -0.04 0.06 -0.04 0.08 -0.02 -0.13 0.08 0.00
SEPR33 -0.02 -0.03 0.02 0.02 0.69 0.05 0.02 0.01 0.02 -0.04 -0.07 0.10 0.09
SEPR34 -0.04 -0.03 -0.01 -0.05 0.83 0.05 -0.05 0.06 -0.03 0.02 0.11 0.00 -0.13
EXCITE35 0.11 -0.12 0.01 -0.11 0.16 0.01 0.05 -0.09 0.65 0.02 -0.04 -0.01 0.10
EXCITE36 -0.01 0.20 0.04 0.01 -0.06 0.00 -0.06 0.01 0.72 0.02 -0.09 0.04 -0.01
EXCITE37 -0.01 -0.07 -0.03 0.03 0.02 0.03 0.03 -0.02 0.79 -0.03 0.02 -0.05 -0.05
EXCITE38 -0.03 0.04 -0.12 0.05 -0.04 0.03 -0.01 0.08 0.77 -0.07 0.07 -0.01 -0.08
ATT39 0.09 -0.04 0.15 -0.17 0.11 -0.31 0.03 -0.11 0.24 0.14 -0.01 0.10 0.22
ATT40 0.06 -0.17 0.36 -0.05 0.14 -0.17 -0.01 0.03 0.12 0.07 0.07 0.12 0.01
ATT41 -0.03 0.00 0.19 0.05 0.15 -0.18 0.01 -0.01 0.13 0.01 0.17 0.08 0.34
ATT42 0.00 -0.04 0.19 0.02 0.18 -0.07 0.08 0.05 0.17 0.01 0.23 0.05 0.25
PLAY43 -0.26 0.52 0.00 -0.03 -0.08 -0.06 -0.03 0.03 0.07 -0.27 0.06 -0.01 0.09
PLAY44 -0.03 0.87 0.00 -0.03 -0.01 0.01 0.07 -0.02 0.06 -0.04 -0.05 0.04 -0.03
PLAY45 0.02 0.83 -0.01 -0.11 -0.07 -0.09 -0.02 -0.05 0.02 0.03 0.04 0.04 0.01
PLAY46 -0.05 0.75 -0.16 -0.02 0.03 0.04 -0.06 0.01 0.04 0.09 -0.02 -0.03 -0.11
IMP47 0.07 0.30 -0.02 0.03 0.06 0.35 0.00 0.00 0.15 0.04 0.30 0.05 0.09
IMP48 0.02 0.22 0.05 0.18 0.07 0.25 0.02 0.03 0.12 0.02 0.23 0.08 0.20
IMP49 0.04 0.08 0.10 0.20 -0.05 0.36 -0.04 -0.06 0.14 0.00 0.24 0.08 -0.03
MISC50 0.04 0.09 0.08 0.26 0.28 0.09 -0.07 0.05 0.09 -0.06 0.21 -0.15 -0.05
MISC51 -0.13 -0.09 0.10 0.06 0.30 0.22 -0.02 -0.03 0.06 0.08 0.30 -0.11 -0.09
MISC52 -0.13 -0.24 0.02 0.01 -0.07 0.00 -0.08 0.05 0.09 0.17 0.45 0.28 0.19
MISC53 -0.17 -0.19 -0.07 0.19 0.03 0.14 -0.11 -0.02 0.04 0.07 0.43 0.19 0.18
MISC54 -0.03 -0.08 0.14 -0.03 -0.04 0.00 -0.03 0.67 0.06 0.00 0.04 0.15 -0.06
MISC55 -0.02 0.00 -0.09 -0.07 0.03 -0.01 0.05 0.91 0.00 0.02 -0.03 -0.04 0.02
MISC56 -0.02 -0.03 0.02 0.11 -0.03 0.02 -0.02 0.71 -0.04 0.00 0.04 -0.02 -0.02
MISC57 -0.04 0.09 0.10 0.15 0.18 0.25 0.01 -0.01 0.11 -0.03 0.16 -0.06 0.16
MISC58 -0.01 0.10 0.02 0.34 0.28 0.06 0.00 0.06 -0.09 -0.01 0.06 -0.14 0.05
MISC59 0.08 0.30 0.15 0.12 0.42 0.12 -0.05 0.02 0.00 -0.02 0.15 -0.06 0.25
MISC60 0.07 0.34 0.11 -0.01 0.13 0.02 -0.07 0.00 0.15 0.02 0.07 -0.11 0.34
MISC61 0.08 0.43 0.05 0.02 0.23 -0.02 -0.02 -0.07 0.18 0.09 -0.02 -0.19 0.29
MISC62 0.00 0.03 0.45 -0.03 -0.05 0.05 0.40 -0.01 0.05 -0.01 0.14 -0.02 0.10
MISC63 -0.01 0.05 0.44 0.06 -0.11 0.03 0.07 0.10 0.15 0.04 0.21 -0.02 0.12
MISC64 -0.13 -0.06 0.76 0.02 0.04 0.02 0.00 -0.01 -0.04 0.03 -0.02 0.02 -0.09
MISC65 -0.10 -0.06 0.69 -0.03 0.04 0.11 0.11 0.00 -0.04 0.00 0.08 0.05 -0.04
MISC66 0.20 -0.06 0.60 -0.01 0.03 0.10 -0.07 0.19 -0.07 0.01 -0.05 0.07 0.04
MISC67 0.19 -0.10 0.56 0.05 0.06 0.00 0.00 0.17 -0.06 0.00 -0.07 0.05 0.09
MISC69 0.04 -0.03 0.11 0.06 0.14 -0.01 0.03 0.23 0.07 -0.01 0.25 -0.22 -0.09
MISC70 -0.03 0.08 0.01 0.08 0.19 0.04 0.10 0.12 0.01 0.20 0.30 -0.07 0.22
MISC71 0.00 0.05 0.24 -0.03 0.16 -0.06 -0.11 0.19 -0.04 0.05 0.32 -0.06 0.06
2.3.6.4.1 13 Factor Model Largest Loading Per Item
Largest Loading Per Item and Associated Factors, Sorted by Factor
largest maximum itemNames itemDescriptions
14 PA1 0.36 ATT40 Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
47 PA1 0.45 MISC62 Becomes highly excited and/or distracted when encountering unfamiliar dogs
48 PA1 0.44 MISC63 Becomes highly excited and/or distracted when encountering unfamiliar people
49 PA1 0.76 MISC64 When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
50 PA1 0.69 MISC65 Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
51 PA1 0.60 MISC66 Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
52 PA1 0.56 MISC67 Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
69 PA1 0.60 TRAIN07 Unfocused; is easily distracted by interesting sights, sounds or smells
70 PA1 0.11 TRAIN08 Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
26 PA10 0.43 FEAR26 When examined/treated by a veterinarian
29 PA10 0.65 FEAR29 When having nails trimmed, or feet touched/handled
30 PA10 0.62 FEAR30 When groomed or bathed
36 PA11 0.30 MISC51 Escapes or would escape from home, yard or kennel given the chance
37 PA11 0.45 MISC52 Begs persistently for food when people are eating
38 PA11 0.43 MISC53 Steals food
53 PA11 0.25 MISC69 Chases/follows shadows, light spots, etc.
54 PA11 0.30 MISC70 Barks persistently when alarmed or excited
55 PA11 0.32 MISC71 Licks people or objects excessively
21 PA12 0.82 FEAR21 When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
23 PA12 0.82 FEAR23 When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
24 PA12 0.86 FEAR24 When an unfamiliar person tries to touch or pet the dog
28 PA12 0.46 FEAR28 When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
31 PA12 0.37 FEAR31 When barked, growled, or lunged at by an unfamiliar dog
32 PA13 0.35 IMP47 Impulsive; doesn’t seem to think before s/he acts
33 PA13 0.25 IMP48 Becomes frustrated/impatient in a wide range of situations
34 PA13 0.36 IMP49 Is difficult to interrupt or distract when doing things s/he wants to do
42 PA13 0.25 MISC57 Pulls excessively hard when on leash
63 PA13 0.53 TRAIN01 Is hard to recall when off the leash
64 PA13 0.59 TRAIN02 Is slow to obey a ‘sit’ command
65 PA13 0.66 TRAIN03 Is slow to obey a ‘stay’ command
66 PA13 0.65 TRAIN04 Has difficulty attending/listening to things you say or do
67 PA13 0.45 TRAIN05 Is slow to respond to corrections or reprimands: thick-skinned
68 PA13 0.37 TRAIN06 Is slow to learn new tricks or tasks
46 PA2 0.43 MISC61 Active, energetic, always on the go
56 PA2 0.52 PLAY43 Eagerly engages in play with new/unfamiliar people
57 PA2 0.87 PLAY44 Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
58 PA2 0.83 PLAY45 Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
59 PA2 0.75 PLAY46 Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1 PA3 0.62 AGG09 Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2 PA3 0.66 AGG10 Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6 PA3 0.56 AGG14 When strangers walk past when the dog is in his/her home run or kennel
7 PA3 0.66 AGG15 When an unfamiliar person tries to touch or pet the dog
9 PA3 0.26 AGG17 When stared at directly by you or another familiar person
3 PA4 0.80 AGG11 Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4 PA4 0.87 AGG12 When you or another familiar person approaches the dog directly while s/he is eating
5 PA4 0.94 AGG13 When his/her food is taken away by you or another familiar person
12 PA4 0.44 AGG20 When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
43 PA4 0.34 MISC58 Urinates against objects/furnishings indoors
22 PA5 0.30 FEAR22 In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
25 PA5 0.33 FEAR25 In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
39 PA5 0.67 MISC54 Reluctant to/nervous about crossing grates or other unfamiliar surfaces
40 PA5 0.91 MISC55 Reluctant to/nervous about crossing shiny or slippery floors
41 PA5 0.71 MISC56 Nervous or frightened when ascending or descending some types of stairs
35 PA6 0.28 MISC50 NA
44 PA6 0.42 MISC59 Hyperactive, restless, has trouble settling down
60 PA6 0.79 SEPR32 Restlessness/agitation/pacing when left alone
61 PA6 0.69 SEPR33 Barking or whining when left alone
62 PA6 0.83 SEPR34 Chewing/scratching at doors, floor, fencing, etc., when left alone
15 PA7 0.34 ATT41 Tends to nudge or paw you (or others) for attention
16 PA7 0.25 ATT42 Becomes agitated (whines, jumps up, tries to intervene) when attention is given to another person or animal
45 PA7 0.34 MISC60 Playful, puppyish, boisterous
8 PA8 0.82 AGG16 When approached directly by an unfamiliar dog while being walked/exercised on a leash
10 PA8 0.79 AGG18 When barked, growled, or lunged at by another dog
11 PA8 0.64 AGG19 Towards other familiar dogs
27 PA8 0.48 FEAR27 When approached directly by an unfamiliar dog
13 PA9 0.24 ATT39 Displays a strong attachment for you or another familiar person
17 PA9 0.65 EXCITE35 Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
18 PA9 0.72 EXCITE36 Excitable when playing with you or other familiar persons
19 PA9 0.79 EXCITE37 Excitable just before being taken out for a walk
20 PA9 0.77 EXCITE38 Excitable just before being taken out for work or training

2.3.7 13 Model Reliability Measures

The overall alpha for all items is 0.8884139.

The overall omega for all items is 0.9288948.

Hierarchical omega is 0.5686546.

2.4 14 Factors

2.4.1 Imputation of Missing Items (14 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.4.2 14-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.4.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.5549798^{4} with 2278 DF, p = 0e+00.

2.4.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8563417

2.4.3 14-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.4.3.1 Bartlett’s Test of Sphericity

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.0057354^{4} with 2278 DF, p = 0e+00.

2.4.3.2 14-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8563417

2.4.4 Between-Item Correlations

2.4.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.7175082. The maximum correlation in this data set is 0.8881154.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.6902317. The maximum correlation was 0.8871507.

2.4.5 Estimating Number of Factors

2.4.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

The suggested number of factors is 16.

2.4.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
Number of Factors MAP value
1 0.0247
2 0.0208
3 0.0162
4 0.0147
5 0.0139
6 0.0130
7 0.0124
8 0.0120
9 0.0117
10 0.0116
11 0.0112
12 0.0109
13 0.0111
14 0.0114
15 0.0116
16 0.0119
17 0.0122
18 0.0125

2.4.6 Factor Analysis for 14 Factors

2.4.6.1 14 Factors Model Fit

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

  • chi-square: 2.0575826^{4}
  • degrees of freedom: 1417
  • P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.4621591. Should be > 0.9; need reference)

2.4.6.2 14 Factor Model Communalities

fanal14.communality
TRAIN01 0.41
TRAIN02 0.27
TRAIN04 0.63
TRAIN05 0.35
TRAIN06 0.27
TRAIN07 0.61
TRAIN08 0.63
AGG09 0.76
AGG10 0.66
AGG11 0.78
AGG12 0.78
AGG13 0.96
AGG14 0.50
AGG15 0.80
AGG16 0.74
AGG17 0.63
AGG18 0.72
AGG19 0.69
AGG20 0.60
FEAR21 0.82
FEAR22 0.39
FEAR23 0.80
FEAR24 0.86
FEAR25 0.49
FEAR26 0.44
FEAR27 0.82
FEAR28 0.67
FEAR29 0.52
FEAR30 0.57
FEAR31 0.70
SEPR32 0.68
SEPR33 0.53
SEPR34 0.71
EXCITE35 0.50
EXCITE36 0.62
EXCITE37 0.60
EXCITE38 0.62
ATT39 0.34
ATT40 0.40
ATT41 0.39
ATT42 0.36
PLAY43 0.55
PLAY44 0.82
PLAY45 0.75
PLAY46 0.71
IMP47 0.49
IMP48 0.45
IMP49 0.40
MISC50 0.35
MISC52 0.43
MISC53 0.42
MISC54 0.62
MISC55 0.72
MISC56 0.59
MISC57 0.35
MISC58 0.26
MISC59 0.57
MISC60 0.54
MISC61 0.68
MISC62 0.53
MISC63 0.38
MISC64 0.58
MISC65 0.61
MISC66 0.67
MISC67 0.58
MISC69 0.22
MISC70 0.36
MISC71 0.27

2.4.6.3 How many communalities < 0.40?

There are 16 items with communality < 0.40.

fanal14.communality item
TRAIN02 0.27 TRAIN02
TRAIN05 0.35 TRAIN05
TRAIN06 0.27 TRAIN06
FEAR22 0.39 FEAR22
ATT39 0.34 ATT39
ATT40 0.40 ATT40
ATT41 0.39 ATT41
ATT42 0.36 ATT42
IMP49 0.40 IMP49
MISC50 0.35 MISC50
MISC57 0.35 MISC57
MISC58 0.26 MISC58
MISC63 0.38 MISC63
MISC69 0.22 MISC69
MISC70 0.36 MISC70
MISC71 0.27 MISC71

2.4.6.4 14 Factor Model Loadings

PA2 PA11 PA1 PA4 PA3 PA6 PA5 PA12 PA9 PA8 PA14 PA7 PA10 PA13
TRAIN01 -0.14 -0.14 0.17 -0.02 0.06 0.04 -0.08 0.50 -0.03 0.01 0.00 -0.04 0.12 0.03
TRAIN02 -0.06 0.03 0.06 -0.08 0.01 0.04 0.03 0.46 0.09 0.00 0.01 -0.03 0.11 -0.02
TRAIN04 -0.06 0.07 0.26 0.01 -0.05 0.07 -0.02 0.66 0.03 -0.02 0.02 -0.08 -0.04 -0.05
TRAIN05 0.02 -0.09 0.10 0.14 0.10 0.01 -0.03 0.48 0.07 0.06 -0.08 0.03 -0.11 0.01
TRAIN06 -0.06 -0.01 0.19 -0.04 -0.08 0.10 0.10 0.32 -0.01 -0.01 0.10 -0.06 -0.03 -0.17
TRAIN07 -0.14 0.07 0.58 -0.02 -0.10 0.04 -0.05 0.30 0.00 0.05 -0.01 -0.04 0.05 -0.03
TRAIN08 -0.73 -0.01 0.10 0.03 -0.01 0.02 0.06 0.03 0.05 -0.11 0.07 -0.01 0.04 0.00
AGG09 0.07 0.25 0.12 0.11 0.71 -0.04 0.03 0.00 -0.05 0.01 0.03 -0.01 -0.05 0.02
AGG10 0.06 0.01 -0.03 0.04 0.74 0.08 -0.04 -0.04 0.00 0.12 -0.02 0.02 0.05 -0.04
AGG11 -0.10 -0.05 -0.10 0.81 0.01 0.12 -0.02 0.04 -0.11 0.05 0.06 0.00 0.05 0.07
AGG12 -0.06 0.09 0.03 0.86 -0.04 -0.03 0.03 -0.04 0.06 0.06 0.00 0.00 -0.06 -0.05
AGG13 0.01 0.03 0.04 0.93 0.07 -0.10 -0.02 0.01 0.05 0.03 -0.02 0.01 0.08 -0.01
AGG14 -0.02 0.06 -0.01 -0.08 0.63 0.10 0.03 0.02 0.04 0.12 -0.03 0.17 -0.04 -0.10
AGG15 -0.08 0.27 -0.05 0.09 0.70 -0.06 0.04 0.03 -0.04 0.11 -0.10 -0.08 0.10 0.12
AGG16 -0.02 -0.06 0.09 -0.03 0.28 -0.05 0.03 0.01 0.00 0.60 0.30 -0.03 -0.07 -0.02
AGG17 0.19 -0.01 0.10 0.24 0.41 0.25 0.13 -0.02 0.13 -0.03 0.04 -0.28 0.11 -0.26
AGG18 0.04 -0.10 0.05 -0.03 0.30 0.00 -0.02 0.00 -0.03 0.60 0.28 0.02 -0.04 0.01
AGG19 0.07 -0.01 0.00 0.17 0.03 0.06 0.03 -0.02 0.09 0.71 0.02 -0.08 0.06 0.04
AGG20 0.03 0.00 -0.07 0.31 -0.12 0.06 0.02 0.02 -0.02 0.61 -0.09 0.14 0.10 -0.12
FEAR21 -0.01 0.80 -0.01 0.07 0.11 0.03 0.02 0.01 0.01 -0.03 0.10 -0.02 0.07 0.00
FEAR22 -0.08 0.35 0.10 -0.07 -0.25 0.02 0.28 0.00 0.03 0.22 -0.11 0.09 0.11 -0.05
FEAR23 -0.02 0.78 -0.01 0.00 0.16 0.04 0.05 0.01 -0.01 0.00 0.13 0.00 -0.05 0.02
FEAR24 -0.10 0.80 -0.01 0.07 0.14 -0.02 -0.03 -0.05 0.03 -0.05 0.16 0.00 0.03 0.02
FEAR25 0.06 0.35 0.20 0.10 -0.12 0.03 0.32 0.10 0.01 0.06 0.03 0.13 -0.02 -0.09
FEAR26 0.04 0.33 -0.01 0.06 0.04 0.06 -0.02 0.01 -0.01 0.02 0.10 0.00 0.43 0.03
FEAR27 0.01 0.16 -0.03 0.03 -0.04 -0.01 0.02 0.00 -0.01 0.08 0.82 -0.01 0.02 -0.01
FEAR28 0.06 0.49 0.12 0.00 -0.09 0.04 0.38 0.01 0.05 0.01 0.03 -0.04 0.17 -0.05
FEAR29 0.01 -0.04 0.04 0.00 0.06 0.05 -0.02 0.00 0.02 -0.02 0.07 -0.01 0.69 -0.01
FEAR30 0.07 -0.01 0.05 0.09 -0.04 0.12 0.12 -0.02 -0.03 0.05 0.06 0.03 0.63 -0.04
FEAR31 -0.01 0.11 -0.01 -0.02 -0.12 0.02 0.05 0.00 0.01 0.02 0.76 0.01 0.11 -0.04
SEPR32 -0.04 0.11 0.02 -0.06 -0.02 0.79 -0.06 -0.07 0.08 0.09 -0.02 -0.03 0.06 0.01
SEPR33 -0.05 -0.01 0.03 0.01 -0.06 0.68 -0.01 0.01 0.03 0.04 -0.02 0.03 0.08 0.06
SEPR34 -0.03 -0.09 -0.03 -0.02 0.08 0.82 0.07 0.07 -0.03 -0.07 0.03 0.01 0.02 0.03
EXCITE35 -0.15 0.11 0.02 -0.11 -0.01 0.14 -0.09 -0.03 0.63 0.06 -0.01 0.04 0.00 0.11
EXCITE36 0.17 0.01 0.05 0.00 0.00 -0.06 0.01 -0.01 0.71 -0.01 -0.09 -0.04 0.06 0.07
EXCITE37 -0.08 -0.04 -0.04 0.04 0.01 0.04 -0.01 0.04 0.78 0.00 0.04 -0.01 -0.04 0.02
EXCITE38 0.04 -0.04 -0.13 0.05 -0.04 -0.03 0.09 0.06 0.76 0.01 0.02 0.03 -0.01 -0.02
ATT39 0.03 0.09 0.21 -0.11 0.11 0.10 -0.15 -0.38 0.20 -0.04 0.02 0.28 -0.01 -0.02
ATT40 -0.02 0.06 0.41 0.03 0.08 0.16 0.00 -0.19 0.08 -0.09 0.07 0.27 0.01 -0.22
ATT41 0.07 0.05 0.19 0.06 -0.09 0.11 -0.06 -0.18 0.07 0.05 -0.03 0.52 -0.03 0.01
ATT42 -0.03 0.03 0.14 0.00 -0.03 0.14 0.02 -0.01 0.12 0.09 0.05 0.42 -0.02 0.06
PLAY43 0.49 -0.29 -0.01 -0.01 -0.27 -0.08 0.04 -0.05 0.07 -0.07 0.08 0.03 -0.01 0.13
PLAY44 0.88 -0.02 0.03 -0.02 -0.03 -0.01 -0.03 0.02 0.05 0.05 0.03 -0.03 0.02 0.04
PLAY45 0.81 0.00 -0.01 -0.09 0.05 -0.07 -0.04 -0.06 0.01 -0.05 0.04 0.04 0.03 0.09
PLAY46 0.75 -0.03 -0.15 -0.01 0.10 0.04 0.01 0.07 0.04 -0.02 -0.09 -0.06 -0.01 0.03
IMP47 0.26 0.07 -0.09 -0.03 0.04 0.04 -0.01 0.47 0.13 0.01 0.06 0.28 0.05 0.06
IMP48 0.20 0.05 -0.02 0.11 -0.01 0.06 0.01 0.36 0.10 0.06 0.03 0.33 0.05 0.06
IMP49 0.08 0.01 0.07 0.18 0.03 -0.03 -0.06 0.44 0.14 -0.06 0.08 0.17 0.08 -0.04
MISC50 0.13 -0.04 0.07 0.31 0.00 0.30 0.05 0.14 0.08 -0.16 0.13 0.13 -0.17 -0.01
MISC52 -0.25 -0.14 -0.06 0.00 0.14 -0.10 0.05 0.07 0.06 -0.10 0.07 0.47 0.25 0.04
MISC53 -0.20 -0.18 -0.12 0.16 0.02 0.01 -0.02 0.20 0.02 -0.09 0.04 0.42 0.17 0.06
MISC54 -0.06 0.00 0.13 -0.04 0.00 -0.03 0.66 0.01 0.07 0.00 0.02 0.05 0.14 -0.10
MISC55 -0.01 0.02 -0.07 -0.08 0.02 0.03 0.87 -0.04 0.01 0.06 -0.01 -0.01 -0.03 0.00
MISC56 -0.07 -0.08 0.01 0.14 0.04 -0.02 0.73 -0.02 -0.02 -0.09 0.09 -0.06 0.01 0.08
MISC57 -0.02 -0.05 0.06 0.11 -0.06 0.15 0.00 0.27 0.09 0.04 0.00 0.13 0.00 0.27
MISC58 0.05 -0.04 0.01 0.35 0.00 0.26 0.07 0.06 -0.10 0.00 0.01 0.02 -0.11 0.17
MISC59 0.18 0.09 0.06 0.05 -0.07 0.37 0.04 0.19 -0.03 0.03 -0.04 0.20 0.00 0.34
MISC60 0.12 0.01 0.08 0.00 -0.03 0.05 0.02 -0.05 0.14 -0.10 0.01 0.03 0.01 0.62
MISC61 0.20 0.06 0.02 0.01 0.02 0.15 -0.04 -0.07 0.17 0.01 -0.10 -0.05 -0.06 0.63
MISC62 -0.07 -0.10 0.40 -0.04 0.07 -0.08 0.01 0.07 0.04 0.24 0.28 0.04 0.03 0.26
MISC63 -0.03 -0.04 0.37 0.05 0.06 -0.14 0.13 0.08 0.12 0.02 0.10 0.17 0.02 0.21
MISC64 -0.07 -0.14 0.70 0.05 0.07 0.06 0.03 0.05 -0.05 -0.03 0.00 -0.04 0.05 0.03
MISC65 -0.08 -0.11 0.63 -0.02 0.04 0.04 0.03 0.15 -0.06 0.06 0.07 0.06 0.07 0.05
MISC66 -0.06 0.25 0.57 -0.03 -0.03 0.03 0.19 0.11 -0.07 -0.02 -0.03 0.05 0.08 0.00
MISC67 -0.12 0.24 0.52 0.03 -0.04 0.05 0.17 0.02 -0.07 0.04 -0.02 0.07 0.05 0.04
MISC69 0.01 -0.01 0.07 0.09 0.06 0.15 0.23 0.08 0.04 -0.04 0.14 0.16 -0.23 -0.05
MISC70 0.00 -0.01 -0.09 0.01 0.18 0.15 0.13 0.15 -0.02 0.12 -0.01 0.34 -0.05 0.22
MISC71 0.04 -0.06 0.17 0.02 0.07 0.15 0.21 0.00 -0.08 -0.17 0.11 0.26 -0.06 0.11
2.4.6.4.1 14 Factor Model Largest Loading Per Item
Largest Loading Per Item and Associated Factors, Sorted by Factor
largest maximum itemNames itemDescriptions
14 PA1 0.41 ATT40 Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
46 PA1 0.40 MISC62 Becomes highly excited and/or distracted when encountering unfamiliar dogs
47 PA1 0.37 MISC63 Becomes highly excited and/or distracted when encountering unfamiliar people
48 PA1 0.70 MISC64 When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
49 PA1 0.63 MISC65 Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
50 PA1 0.57 MISC66 Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
51 PA1 0.52 MISC67 Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
67 PA1 0.58 TRAIN07 Unfocused; is easily distracted by interesting sights, sounds or smells
68 PA1 0.10 TRAIN08 Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
26 PA10 0.43 FEAR26 When examined/treated by a veterinarian
29 PA10 0.69 FEAR29 When having nails trimmed, or feet touched/handled
30 PA10 0.63 FEAR30 When groomed or bathed
21 PA11 0.80 FEAR21 When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
22 PA11 0.35 FEAR22 In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
23 PA11 0.78 FEAR23 When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
24 PA11 0.80 FEAR24 When an unfamiliar person tries to touch or pet the dog
25 PA11 0.35 FEAR25 In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
28 PA11 0.49 FEAR28 When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
32 PA12 0.47 IMP47 Impulsive; doesn’t seem to think before s/he acts
33 PA12 0.36 IMP48 Becomes frustrated/impatient in a wide range of situations
34 PA12 0.44 IMP49 Is difficult to interrupt or distract when doing things s/he wants to do
41 PA12 0.27 MISC57 Pulls excessively hard when on leash
62 PA12 0.50 TRAIN01 Is hard to recall when off the leash
63 PA12 0.46 TRAIN02 Is slow to obey a ‘sit’ command
64 PA12 0.66 TRAIN04 Has difficulty attending/listening to things you say or do
65 PA12 0.48 TRAIN05 Is slow to respond to corrections or reprimands: thick-skinned
66 PA12 0.32 TRAIN06 Is slow to learn new tricks or tasks
44 PA13 0.62 MISC60 Playful, puppyish, boisterous
45 PA13 0.63 MISC61 Active, energetic, always on the go
27 PA14 0.82 FEAR27 When approached directly by an unfamiliar dog
31 PA14 0.76 FEAR31 When barked, growled, or lunged at by an unfamiliar dog
55 PA2 0.49 PLAY43 Eagerly engages in play with new/unfamiliar people
56 PA2 0.88 PLAY44 Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
57 PA2 0.81 PLAY45 Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
58 PA2 0.75 PLAY46 Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1 PA3 0.71 AGG09 Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2 PA3 0.74 AGG10 Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6 PA3 0.63 AGG14 When strangers walk past when the dog is in his/her home run or kennel
7 PA3 0.70 AGG15 When an unfamiliar person tries to touch or pet the dog
9 PA3 0.41 AGG17 When stared at directly by you or another familiar person
3 PA4 0.81 AGG11 Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4 PA4 0.86 AGG12 When you or another familiar person approaches the dog directly while s/he is eating
5 PA4 0.93 AGG13 When his/her food is taken away by you or another familiar person
35 PA4 0.31 MISC50 NA
42 PA4 0.35 MISC58 Urinates against objects/furnishings indoors
38 PA5 0.66 MISC54 Reluctant to/nervous about crossing grates or other unfamiliar surfaces
39 PA5 0.87 MISC55 Reluctant to/nervous about crossing shiny or slippery floors
40 PA5 0.73 MISC56 Nervous or frightened when ascending or descending some types of stairs
52 PA5 0.23 MISC69 Chases/follows shadows, light spots, etc.
43 PA6 0.37 MISC59 Hyperactive, restless, has trouble settling down
59 PA6 0.79 SEPR32 Restlessness/agitation/pacing when left alone
60 PA6 0.68 SEPR33 Barking or whining when left alone
61 PA6 0.82 SEPR34 Chewing/scratching at doors, floor, fencing, etc., when left alone
13 PA7 0.28 ATT39 Displays a strong attachment for you or another familiar person
15 PA7 0.52 ATT41 Tends to nudge or paw you (or others) for attention
16 PA7 0.42 ATT42 Becomes agitated (whines, jumps up, tries to intervene) when attention is given to another person or animal
36 PA7 0.47 MISC52 Begs persistently for food when people are eating
37 PA7 0.42 MISC53 Steals food
53 PA7 0.34 MISC70 Barks persistently when alarmed or excited
54 PA7 0.26 MISC71 Licks people or objects excessively
8 PA8 0.60 AGG16 When approached directly by an unfamiliar dog while being walked/exercised on a leash
10 PA8 0.60 AGG18 When barked, growled, or lunged at by another dog
11 PA8 0.71 AGG19 Towards other familiar dogs
12 PA8 0.61 AGG20 When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
17 PA9 0.63 EXCITE35 Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
18 PA9 0.71 EXCITE36 Excitable when playing with you or other familiar persons
19 PA9 0.78 EXCITE37 Excitable just before being taken out for a walk
20 PA9 0.76 EXCITE38 Excitable just before being taken out for work or training

2.4.7 14 Model Reliability Measures

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

The overall alpha for all items is 0.8848002.

The overall omega for all items is 0.929246.

Hierarchical omega is 0.5714398.

2.5 15 Factors

2.5.1 Imputation of Missing Items (15 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.5.2 15-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.5.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.6065968^{4} with 2278 DF, p = 0e+00.

2.5.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8584491

2.5.3 15-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.5.3.1 Bartlett’s Test of Sphericity

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.0550218^{4} with 2278 DF, p = 0e+00.

2.5.3.2 15-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8584491

2.5.4 Between-Item Correlations

2.5.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.7175949. The maximum correlation in this data set is 0.8888165.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.6902169. The maximum correlation was 0.8867879.

2.5.5 Estimating Number of Factors

2.5.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

The suggested number of factors is 15.

2.5.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
Number of Factors MAP value
1 0.0252
2 0.0213
3 0.0163
4 0.0146
5 0.0138
6 0.0130
7 0.0127
8 0.0121
9 0.0118
10 0.0116
11 0.0113
12 0.0110
13 0.0113
14 0.0115
15 0.0117
16 0.0120
17 0.0122
18 0.0126

2.5.6 Factor Analysis for 15 Factors

2.5.6.1 15 Factors Model Fit

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

  • chi-square: 1.9648324^{4}
  • degrees of freedom: 1363
  • P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.4705202. Should be > 0.9; need reference)

2.5.6.2 15 Factor Model Communalities

fanal15.communality
TRAIN01 0.56
TRAIN02 0.42
TRAIN03 0.52
TRAIN04 0.61
TRAIN05 0.34
TRAIN06 0.34
TRAIN07 0.61
TRAIN08 0.63
AGG09 0.76
AGG10 0.71
AGG11 0.82
AGG12 0.89
AGG13 0.97
AGG14 0.50
AGG15 0.78
AGG16 0.76
AGG17 0.72
AGG18 0.72
AGG19 0.72
AGG20 0.57
FEAR21 0.83
FEAR22 0.42
FEAR23 0.79
FEAR24 0.86
FEAR25 0.49
FEAR26 0.44
FEAR27 0.82
FEAR28 0.67
FEAR29 0.58
FEAR30 0.59
FEAR31 0.67
SEPR32 0.70
SEPR33 0.60
SEPR34 0.74
EXCITE35 0.49
EXCITE36 0.63
EXCITE37 0.59
EXCITE38 0.63
ATT40 0.27
ATT42 0.27
PLAY43 0.56
PLAY44 0.80
PLAY45 0.74
PLAY46 0.72
IMP47 0.47
IMP48 0.49
IMP49 0.40
MISC50 0.34
MISC51 0.48
MISC52 0.44
MISC53 0.46
MISC54 0.62
MISC55 0.73
MISC56 0.62
MISC57 0.35
MISC58 0.25
MISC59 0.57
MISC60 0.58
MISC61 0.69
MISC62 0.52
MISC63 0.40
MISC64 0.59
MISC65 0.63
MISC66 0.69
MISC67 0.62
MISC68 0.24
MISC70 0.36
MISC71 0.29

2.5.6.3 How many communalities < 0.40?

There are 12 items with communality < 0.40.

fanal15.communality item
TRAIN05 0.34 TRAIN05
TRAIN06 0.34 TRAIN06
ATT40 0.27 ATT40
ATT42 0.27 ATT42
IMP49 0.40 IMP49
MISC50 0.34 MISC50
MISC57 0.35 MISC57
MISC58 0.25 MISC58
MISC63 0.40 MISC63
MISC68 0.24 MISC68
MISC70 0.36 MISC70
MISC71 0.29 MISC71

2.5.6.4 15 Factor Model Loadings

PA1 PA15 PA2 PA5 PA3 PA6 PA12 PA7 PA9 PA8 PA11 PA13 PA14 PA10 PA4
TRAIN01 0.13 -0.02 -0.11 -0.10 -0.05 -0.07 0.48 -0.08 -0.06 0.10 0.10 -0.06 0.04 0.10 0.36
TRAIN02 -0.05 -0.01 -0.02 -0.02 0.07 0.02 0.64 0.08 0.04 -0.05 -0.04 0.02 -0.01 0.09 -0.10
TRAIN03 -0.07 -0.01 -0.07 -0.08 0.00 0.08 0.69 0.07 0.04 0.08 0.03 -0.08 0.06 0.08 -0.06
TRAIN04 0.25 0.05 0.00 0.07 -0.05 0.03 0.62 -0.01 -0.01 -0.06 -0.02 0.04 -0.05 -0.06 0.09
TRAIN05 0.09 -0.11 0.06 0.18 0.10 -0.02 0.43 -0.02 0.05 0.03 0.07 -0.05 0.02 -0.13 0.09
TRAIN06 0.12 -0.07 -0.03 0.04 -0.02 0.12 0.44 0.14 -0.05 -0.06 -0.10 0.12 -0.17 -0.04 -0.13
TRAIN07 0.59 0.05 -0.12 0.01 -0.10 0.03 0.28 -0.06 -0.01 0.02 -0.08 0.01 -0.02 0.04 0.04
TRAIN08 0.09 0.02 -0.72 0.02 -0.03 0.01 0.07 0.07 0.04 -0.09 0.01 0.05 0.00 0.04 0.05
AGG09 0.07 0.25 0.05 0.10 0.70 -0.04 0.05 0.05 -0.06 0.02 -0.03 0.02 0.05 -0.03 0.04
AGG10 -0.04 -0.04 0.06 0.07 0.79 0.10 -0.01 -0.02 0.00 0.07 0.01 0.00 -0.05 0.05 -0.03
AGG11 -0.15 0.04 -0.11 0.72 -0.07 0.06 0.04 0.01 -0.14 0.16 0.06 0.01 0.11 0.07 0.25
AGG12 0.04 0.02 -0.06 0.92 0.03 0.04 -0.01 0.03 0.06 0.02 -0.02 0.02 -0.07 -0.05 -0.16
AGG13 0.04 0.01 0.00 0.92 0.09 -0.08 -0.01 -0.01 0.05 0.01 0.01 -0.01 0.01 0.10 0.06
AGG14 0.06 0.06 0.00 -0.08 0.62 0.11 -0.07 0.00 0.06 0.09 0.18 -0.02 -0.12 -0.03 0.03
AGG15 -0.03 0.28 -0.06 0.10 0.68 -0.06 0.02 0.04 -0.05 0.11 0.00 -0.12 0.09 0.08 0.04
AGG16 0.05 -0.06 -0.03 -0.03 0.29 -0.05 0.08 0.05 -0.01 0.61 -0.08 0.28 -0.01 -0.05 -0.06
AGG17 0.11 0.10 0.18 0.14 0.29 0.17 -0.09 0.10 0.14 0.07 -0.23 -0.03 -0.26 0.14 0.42
AGG18 0.03 -0.10 0.03 -0.03 0.30 -0.01 0.04 -0.01 -0.04 0.61 -0.02 0.27 0.03 -0.02 0.00
AGG19 0.00 0.02 0.07 0.12 -0.01 0.03 -0.02 0.02 0.10 0.76 -0.06 0.01 0.02 0.05 0.08
AGG20 -0.02 -0.01 0.06 0.30 -0.11 0.06 -0.04 0.00 0.00 0.59 0.16 -0.06 -0.15 0.08 -0.02
FEAR21 -0.02 0.84 -0.01 0.04 0.07 0.01 0.01 0.01 0.01 -0.01 -0.03 0.08 0.02 0.07 0.04
FEAR22 0.16 0.36 -0.04 -0.07 -0.25 0.03 -0.02 0.23 0.05 0.23 0.11 -0.14 -0.11 0.08 -0.13
FEAR23 0.01 0.76 -0.02 0.01 0.16 0.05 0.00 0.05 0.00 -0.02 -0.03 0.15 0.01 -0.05 -0.02
FEAR24 -0.01 0.82 -0.10 0.05 0.12 -0.02 -0.03 -0.03 0.04 -0.04 -0.03 0.15 0.03 0.03 -0.01
FEAR25 0.25 0.37 0.07 0.07 -0.15 0.01 0.03 0.29 0.04 0.07 0.11 0.03 -0.11 -0.04 0.06
FEAR26 -0.01 0.35 0.05 0.06 0.02 0.05 0.02 -0.01 -0.02 0.02 0.03 0.09 0.03 0.41 -0.01
FEAR27 -0.02 0.19 0.00 0.03 -0.04 0.01 -0.02 0.03 -0.01 0.09 0.00 0.80 -0.02 0.04 0.01
FEAR28 0.14 0.51 0.08 0.00 -0.09 0.03 0.02 0.35 0.05 0.02 -0.02 0.00 -0.08 0.16 -0.07
FEAR29 0.01 -0.04 0.00 0.00 0.05 0.03 0.05 -0.01 0.01 -0.04 0.00 0.06 0.04 0.74 0.03
FEAR30 0.07 -0.01 0.08 0.09 -0.03 0.12 0.00 0.10 -0.03 0.04 0.07 0.04 -0.04 0.64 -0.07
FEAR31 0.00 0.14 -0.01 -0.02 -0.12 0.04 0.00 0.06 0.00 0.04 0.05 0.71 -0.06 0.11 -0.02
SEPR32 0.01 0.08 -0.03 -0.03 0.03 0.81 -0.02 -0.06 0.08 0.06 -0.07 0.00 0.00 0.06 -0.08
SEPR33 0.02 -0.09 -0.04 0.06 0.01 0.73 0.08 0.00 0.01 -0.03 -0.01 0.02 0.06 0.08 -0.13
SEPR34 -0.01 -0.04 -0.02 -0.06 0.03 0.79 0.02 0.07 -0.03 -0.04 0.05 0.02 0.02 0.01 0.22
EXCITE35 0.00 0.10 -0.16 -0.10 0.01 0.14 0.02 -0.09 0.63 0.05 -0.01 0.00 0.13 0.01 -0.04
EXCITE36 0.04 -0.02 0.16 0.03 0.02 -0.05 0.00 0.02 0.71 -0.05 -0.07 -0.06 0.08 0.05 -0.01
EXCITE37 -0.03 -0.01 -0.08 0.04 0.00 0.04 0.02 -0.02 0.77 0.03 0.01 0.02 0.02 -0.04 0.01
EXCITE38 -0.10 0.00 0.05 0.04 -0.07 -0.04 0.01 0.06 0.76 0.04 0.08 0.00 -0.03 -0.01 0.04
ATT40 0.33 0.07 -0.09 -0.03 0.07 0.17 -0.10 0.02 0.10 -0.06 0.11 0.06 -0.14 0.04 -0.02
ATT42 0.16 -0.01 -0.06 -0.01 -0.01 0.15 -0.04 0.04 0.16 0.04 0.26 0.12 0.11 0.00 0.00
PLAY43 0.01 -0.33 0.48 0.01 -0.23 -0.05 -0.06 0.03 0.08 -0.09 0.02 0.10 0.12 -0.01 -0.09
PLAY44 0.00 -0.03 0.85 -0.03 -0.03 -0.01 0.02 -0.03 0.05 0.06 -0.05 0.02 0.06 0.03 -0.01
PLAY45 -0.02 -0.01 0.79 -0.09 0.05 -0.05 -0.08 -0.04 0.02 -0.05 0.01 0.05 0.10 0.02 -0.03
PLAY46 -0.16 0.00 0.75 -0.03 0.06 0.00 0.03 0.01 0.04 0.01 -0.03 -0.10 0.03 -0.02 0.11
IMP47 -0.01 0.07 0.32 0.00 0.04 0.04 0.31 -0.04 0.13 -0.02 0.37 0.09 0.02 0.00 0.05
IMP48 0.08 -0.02 0.26 0.19 0.06 0.11 0.23 -0.01 0.11 -0.03 0.40 0.09 -0.01 -0.01 -0.14
IMP49 0.11 0.04 0.12 0.20 0.00 -0.06 0.32 -0.07 0.13 -0.06 0.25 0.09 -0.05 0.04 0.12
MISC50 0.06 0.01 0.11 0.26 -0.04 0.27 0.09 0.06 0.08 -0.10 0.13 0.11 0.03 -0.14 0.17
MISC51 0.09 -0.02 -0.10 -0.05 -0.03 0.20 0.12 -0.02 0.06 0.10 0.28 -0.03 0.05 -0.08 0.42
MISC52 0.01 -0.09 -0.23 -0.04 0.10 -0.08 -0.05 0.03 0.08 -0.07 0.57 0.06 -0.02 0.19 0.01
MISC53 -0.07 -0.13 -0.17 0.13 0.00 0.01 0.09 -0.04 0.03 -0.06 0.55 0.02 0.00 0.13 0.04
MISC54 0.13 0.02 -0.06 -0.05 -0.02 -0.04 0.02 0.65 0.07 0.01 0.06 0.00 -0.10 0.13 0.02
MISC55 -0.07 -0.01 -0.01 -0.06 0.02 0.02 0.01 0.88 0.00 0.05 -0.03 0.00 0.02 -0.01 -0.02
MISC56 -0.02 -0.07 -0.07 0.13 0.03 -0.03 0.04 0.77 -0.05 -0.06 -0.02 0.06 0.08 0.00 0.03
MISC57 0.09 0.00 0.01 0.09 -0.09 0.11 0.21 -0.02 0.09 0.08 0.19 -0.03 0.25 0.00 0.07
MISC58 0.00 0.04 0.07 0.29 -0.04 0.24 0.06 0.06 -0.11 0.09 0.11 -0.07 0.12 -0.11 0.04
MISC59 0.15 0.11 0.22 0.05 -0.07 0.36 0.07 0.00 -0.03 0.05 0.28 -0.06 0.29 -0.03 -0.03
MISC60 0.05 0.01 0.09 0.00 -0.03 0.03 0.00 0.07 0.11 -0.09 0.00 0.01 0.69 0.03 -0.01
MISC61 0.00 0.09 0.20 -0.01 0.01 0.13 -0.04 -0.03 0.14 0.06 -0.03 -0.13 0.65 -0.04 0.00
MISC62 0.44 -0.09 -0.07 -0.04 0.07 -0.07 0.03 -0.01 0.04 0.25 0.05 0.27 0.24 0.02 -0.02
MISC63 0.44 -0.04 -0.02 0.04 0.07 -0.11 -0.02 0.09 0.15 0.01 0.20 0.10 0.17 0.00 0.00
MISC64 0.73 -0.13 -0.08 0.05 0.05 0.04 0.02 0.00 -0.04 -0.03 -0.09 0.00 0.03 0.06 0.09
MISC65 0.68 -0.08 -0.07 -0.04 0.01 0.03 0.08 -0.02 -0.04 0.08 0.07 0.05 0.02 0.06 0.08
MISC66 0.62 0.22 -0.04 0.00 0.01 0.06 0.08 0.15 -0.06 -0.06 0.04 -0.02 -0.05 0.04 -0.08
MISC67 0.57 0.23 -0.09 0.03 -0.01 0.09 0.00 0.12 -0.06 0.04 0.07 -0.05 -0.03 0.01 -0.15
MISC68 0.08 -0.12 0.06 0.21 0.03 0.08 0.01 0.20 0.07 -0.10 -0.07 0.17 0.04 -0.08 0.28
MISC70 0.03 0.00 0.05 0.01 0.18 0.16 -0.01 0.09 0.00 0.12 0.42 -0.01 0.15 -0.08 -0.02
MISC71 0.23 -0.01 0.03 -0.04 0.03 0.14 -0.10 0.19 -0.04 -0.13 0.28 0.10 0.09 -0.07 0.14
2.5.6.4.1 15 Factor Model Largest Loading Per Item
Largest Loading Per Item and Associated Factors, Sorted by Factor
largest maximum itemNames itemDescriptions
13 PA1 0.33 ATT40 Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
45 PA1 0.44 MISC62 Becomes highly excited and/or distracted when encountering unfamiliar dogs
46 PA1 0.44 MISC63 Becomes highly excited and/or distracted when encountering unfamiliar people
47 PA1 0.73 MISC64 When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
48 PA1 0.68 MISC65 Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
49 PA1 0.62 MISC66 Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
50 PA1 0.57 MISC67 Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
67 PA1 0.59 TRAIN07 Unfocused; is easily distracted by interesting sights, sounds or smells
68 PA1 0.09 TRAIN08 Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
24 PA10 0.41 FEAR26 When examined/treated by a veterinarian
27 PA10 0.74 FEAR29 When having nails trimmed, or feet touched/handled
28 PA10 0.64 FEAR30 When groomed or bathed
14 PA11 0.26 ATT42 Becomes agitated (whines, jumps up, tries to intervene) when attention is given to another person or animal
30 PA11 0.37 IMP47 Impulsive; doesn’t seem to think before s/he acts
31 PA11 0.40 IMP48 Becomes frustrated/impatient in a wide range of situations
35 PA11 0.57 MISC52 Begs persistently for food when people are eating
36 PA11 0.55 MISC53 Steals food
52 PA11 0.42 MISC70 Barks persistently when alarmed or excited
53 PA11 0.28 MISC71 Licks people or objects excessively
32 PA12 0.32 IMP49 Is difficult to interrupt or distract when doing things s/he wants to do
61 PA12 0.48 TRAIN01 Is hard to recall when off the leash
62 PA12 0.64 TRAIN02 Is slow to obey a ‘sit’ command
63 PA12 0.69 TRAIN03 Is slow to obey a ‘stay’ command
64 PA12 0.62 TRAIN04 Has difficulty attending/listening to things you say or do
65 PA12 0.43 TRAIN05 Is slow to respond to corrections or reprimands: thick-skinned
66 PA12 0.44 TRAIN06 Is slow to learn new tricks or tasks
25 PA13 0.80 FEAR27 When approached directly by an unfamiliar dog
29 PA13 0.71 FEAR31 When barked, growled, or lunged at by an unfamiliar dog
40 PA14 0.25 MISC57 Pulls excessively hard when on leash
43 PA14 0.69 MISC60 Playful, puppyish, boisterous
44 PA14 0.65 MISC61 Active, energetic, always on the go
19 PA15 0.84 FEAR21 When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
20 PA15 0.36 FEAR22 In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
21 PA15 0.76 FEAR23 When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
22 PA15 0.82 FEAR24 When an unfamiliar person tries to touch or pet the dog
23 PA15 0.37 FEAR25 In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
26 PA15 0.51 FEAR28 When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
54 PA2 0.48 PLAY43 Eagerly engages in play with new/unfamiliar people
55 PA2 0.85 PLAY44 Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
56 PA2 0.79 PLAY45 Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
57 PA2 0.75 PLAY46 Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1 PA3 0.70 AGG09 Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2 PA3 0.79 AGG10 Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6 PA3 0.62 AGG14 When strangers walk past when the dog is in his/her home run or kennel
7 PA3 0.68 AGG15 When an unfamiliar person tries to touch or pet the dog
9 PA4 0.42 AGG17 When stared at directly by you or another familiar person
34 PA4 0.42 MISC51 Escapes or would escape from home, yard or kennel given the chance
51 PA4 0.28 MISC68 Chases own tail/hind end
3 PA5 0.72 AGG11 Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4 PA5 0.92 AGG12 When you or another familiar person approaches the dog directly while s/he is eating
5 PA5 0.92 AGG13 When his/her food is taken away by you or another familiar person
41 PA5 0.29 MISC58 Urinates against objects/furnishings indoors
33 PA6 0.27 MISC50 NA
42 PA6 0.36 MISC59 Hyperactive, restless, has trouble settling down
58 PA6 0.81 SEPR32 Restlessness/agitation/pacing when left alone
59 PA6 0.73 SEPR33 Barking or whining when left alone
60 PA6 0.79 SEPR34 Chewing/scratching at doors, floor, fencing, etc., when left alone
37 PA7 0.65 MISC54 Reluctant to/nervous about crossing grates or other unfamiliar surfaces
38 PA7 0.88 MISC55 Reluctant to/nervous about crossing shiny or slippery floors
39 PA7 0.77 MISC56 Nervous or frightened when ascending or descending some types of stairs
8 PA8 0.61 AGG16 When approached directly by an unfamiliar dog while being walked/exercised on a leash
10 PA8 0.61 AGG18 When barked, growled, or lunged at by another dog
11 PA8 0.76 AGG19 Towards other familiar dogs
12 PA8 0.59 AGG20 When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
15 PA9 0.63 EXCITE35 Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
16 PA9 0.71 EXCITE36 Excitable when playing with you or other familiar persons
17 PA9 0.77 EXCITE37 Excitable just before being taken out for a walk
18 PA9 0.76 EXCITE38 Excitable just before being taken out for work or training

2.5.7 15 Model Reliability Measures

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

The overall alpha for all items is 0.887826.

The overall omega for all items is 0.9325033.

Hierarchical omega is 0.600543.

2.6 16 Factors

2.6.1 Imputation of Missing Items (16 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.6.2 16-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.6.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.2748245^{4} with 2080 DF, p = 0e+00.

2.6.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.854217

2.6.3 16-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.6.3.1 Bartlett’s Test of Sphericity

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 5.7919248^{4} with 2080 DF, p = 0e+00.

2.6.3.2 16-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.854217

2.6.4 Between-Item Correlations

2.6.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.7175873. The maximum correlation in this data set is 0.8916518.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.6902439. The maximum correlation was 0.8921351.

2.6.5 Estimating Number of Factors

2.6.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

The suggested number of factors is 15.

2.6.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
Number of Factors MAP value
1 0.0262
2 0.0224
3 0.0171
4 0.0153
5 0.0146
6 0.0136
7 0.0131
8 0.0128
9 0.0124
10 0.0124
11 0.0120
12 0.0115
13 0.0116
14 0.0119
15 0.0120
16 0.0125
17 0.0128
18 0.0133

2.6.6 Factor Analysis for 16 Factors

2.6.6.1 16 Factors Model Fit

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

  • chi-square: 1.7661908^{4}
  • degrees of freedom: 1160
  • P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.4646763. Should be > 0.9; need reference)

2.6.6.2 16 Factor Model Communalities

fanal16.communality
TRAIN01 0.56
TRAIN02 0.45
TRAIN03 0.54
TRAIN04 0.61
TRAIN05 0.35
TRAIN06 0.34
TRAIN07 0.62
TRAIN08 0.63
AGG09 0.76
AGG10 0.72
AGG11 0.82
AGG12 0.88
AGG13 0.96
AGG14 0.52
AGG15 0.78
AGG16 0.76
AGG17 0.76
AGG18 0.73
AGG19 0.72
AGG20 0.58
FEAR21 0.83
FEAR22 0.48
FEAR23 0.80
FEAR24 0.86
FEAR25 0.52
FEAR26 0.44
FEAR27 0.83
FEAR28 0.66
FEAR29 0.59
FEAR30 0.59
FEAR31 0.69
SEPR32 0.69
SEPR33 0.63
SEPR34 0.74
EXCITE35 0.50
EXCITE36 0.63
EXCITE37 0.60
EXCITE38 0.63
ATT40 0.30
ATT42 0.27
PLAY43 0.58
PLAY44 0.80
PLAY45 0.77
PLAY46 0.76
IMP47 0.53
IMP48 0.58
MISC51 0.44
MISC52 0.60
MISC53 0.49
MISC54 0.63
MISC55 0.73
MISC56 0.64
MISC57 0.35
MISC58 0.28
MISC59 0.61
MISC60 0.57
MISC61 0.71
MISC62 0.47
MISC64 0.62
MISC65 0.64
MISC66 0.69
MISC67 0.62
MISC69 0.25
MISC70 0.34
MISC71 0.26

2.6.6.3 How many communalities < 0.40?

There are 9 items with communality < 0.40.

fanal16.communality item
TRAIN05 0.35 TRAIN05
TRAIN06 0.34 TRAIN06
ATT40 0.30 ATT40
ATT42 0.27 ATT42
MISC57 0.35 MISC57
MISC58 0.28 MISC58
MISC69 0.25 MISC69
MISC70 0.34 MISC70
MISC71 0.26 MISC71

2.6.6.4 16 Factor Model Loadings

PA12 PA1 PA2 PA5 PA3 PA8 PA11 PA9 PA6 PA15 PA14 PA16 PA10 PA13 PA7 PA4
TRAIN01 -0.03 0.15 -0.08 -0.06 -0.06 -0.05 -0.09 -0.06 0.07 0.47 -0.03 0.03 0.08 0.04 0.11 0.36
TRAIN02 -0.01 -0.01 0.04 0.01 0.10 0.04 0.06 0.04 -0.07 0.66 0.05 -0.04 0.07 -0.02 0.02 -0.12
TRAIN03 0.00 -0.04 -0.03 -0.05 0.02 0.09 0.05 0.04 0.07 0.69 -0.06 0.01 0.06 0.05 0.05 -0.06
TRAIN04 0.06 0.26 -0.02 0.07 -0.06 0.01 -0.02 0.00 -0.06 0.56 0.02 0.18 -0.05 -0.07 -0.06 0.10
TRAIN05 -0.09 0.08 0.04 0.18 0.07 -0.02 -0.02 0.05 0.04 0.38 -0.07 0.19 -0.13 0.00 0.00 0.12
TRAIN06 -0.07 0.11 -0.08 0.01 -0.03 0.10 0.13 -0.04 -0.06 0.38 0.10 0.13 -0.01 -0.18 -0.15 -0.09
TRAIN07 0.06 0.62 -0.10 0.01 -0.10 0.01 -0.08 0.00 0.02 0.26 0.01 0.00 0.02 -0.02 -0.02 0.02
TRAIN08 0.00 0.10 -0.68 0.04 -0.03 0.01 0.08 0.04 -0.10 0.08 0.06 -0.11 0.03 0.02 0.08 0.05
AGG09 0.24 0.04 -0.01 0.07 0.68 -0.06 0.07 -0.06 0.04 0.01 0.00 0.11 0.02 0.05 -0.12 0.08
AGG10 -0.04 -0.01 0.09 0.08 0.80 0.11 -0.03 -0.01 0.06 0.01 0.01 -0.03 0.03 -0.05 0.04 -0.04
AGG11 0.04 -0.12 -0.08 0.74 -0.08 0.06 0.00 -0.13 0.14 0.05 0.02 -0.02 0.07 0.11 0.08 0.23
AGG12 0.02 0.04 -0.05 0.91 0.04 0.04 0.03 0.06 0.01 -0.01 0.03 0.02 -0.06 -0.07 -0.03 -0.16
AGG13 0.01 0.05 0.01 0.92 0.08 -0.07 -0.01 0.05 0.01 -0.01 0.00 0.03 0.08 0.00 0.02 0.04
AGG14 0.08 0.07 0.04 -0.07 0.63 0.12 0.00 0.05 0.11 -0.05 -0.02 0.01 -0.08 -0.11 0.20 0.03
AGG15 0.28 -0.02 -0.04 0.12 0.69 -0.06 0.03 -0.05 0.10 0.03 -0.09 -0.04 0.08 0.09 0.02 0.04
AGG16 -0.08 0.05 -0.06 -0.03 0.29 -0.06 0.06 0.00 0.59 0.05 0.30 0.02 -0.05 0.00 -0.11 -0.02
AGG17 0.08 0.14 0.20 0.17 0.26 0.17 0.11 0.16 0.03 -0.10 0.00 -0.14 0.15 -0.24 -0.16 0.46
AGG18 -0.12 0.01 -0.03 -0.05 0.29 -0.03 0.00 -0.04 0.60 0.01 0.27 0.09 0.01 0.03 -0.09 0.04
AGG19 0.02 0.00 0.06 0.12 0.01 0.02 0.00 0.09 0.77 0.02 0.00 -0.06 0.07 0.03 -0.04 0.04
AGG20 -0.01 -0.03 0.02 0.29 -0.11 0.04 -0.01 -0.01 0.60 -0.06 -0.08 0.11 0.10 -0.14 0.09 -0.03
FEAR21 0.82 -0.02 -0.03 0.04 0.07 0.00 0.01 0.01 -0.02 -0.01 0.09 0.02 0.08 0.02 -0.05 0.06
FEAR22 0.39 0.18 0.05 -0.05 -0.22 0.06 0.21 0.03 0.24 0.05 -0.10 -0.14 0.02 -0.11 0.21 -0.18
FEAR23 0.76 -0.01 -0.03 0.01 0.16 0.05 0.04 0.00 -0.02 0.00 0.15 0.02 -0.04 0.01 -0.06 -0.02
FEAR24 0.81 -0.01 -0.10 0.06 0.13 -0.02 -0.04 0.04 -0.04 -0.03 0.16 0.00 0.04 0.03 -0.02 -0.01
FEAR25 0.41 0.24 0.12 0.07 -0.15 0.04 0.26 0.02 0.10 0.06 0.03 0.01 -0.07 -0.12 0.14 0.02
FEAR26 0.34 0.00 0.04 0.06 0.03 0.04 -0.02 -0.02 0.03 0.02 0.09 0.01 0.42 0.04 0.05 -0.03
FEAR27 0.17 0.00 0.04 0.04 -0.04 0.02 0.02 -0.01 0.07 -0.01 0.82 -0.01 0.01 -0.02 0.04 0.01
FEAR28 0.49 0.13 0.07 0.01 -0.09 0.04 0.35 0.05 0.00 0.02 0.03 0.01 0.16 -0.07 -0.04 -0.05
FEAR29 -0.05 -0.01 -0.05 -0.03 0.02 0.01 0.00 0.01 0.00 0.04 0.03 0.01 0.76 0.03 0.02 0.04
FEAR30 -0.01 0.04 0.04 0.06 -0.05 0.10 0.10 -0.03 0.07 0.00 0.02 0.04 0.65 -0.05 0.07 -0.05
FEAR31 0.11 0.03 0.01 0.00 -0.11 0.04 0.06 0.00 0.01 0.00 0.74 0.01 0.09 -0.05 0.06 -0.02
SEPR32 0.07 0.00 -0.05 -0.04 0.03 0.79 -0.06 0.08 0.04 -0.03 0.00 0.04 0.07 0.00 -0.10 -0.07
SEPR33 -0.08 0.03 -0.01 0.08 0.03 0.76 -0.01 0.01 -0.04 0.09 0.04 -0.02 0.03 0.04 0.01 -0.14
SEPR34 -0.03 -0.01 0.00 -0.04 0.02 0.80 0.06 -0.03 -0.04 0.03 0.02 0.02 0.00 0.02 0.05 0.21
EXCITE35 0.11 0.01 -0.13 -0.10 0.02 0.14 -0.10 0.62 0.04 0.04 0.01 -0.03 -0.01 0.13 0.04 -0.05
EXCITE36 -0.02 0.04 0.14 0.02 0.02 -0.06 0.01 0.71 -0.03 -0.01 -0.08 0.04 0.07 0.09 -0.07 -0.03
EXCITE37 -0.03 -0.03 -0.08 0.05 -0.01 0.03 -0.01 0.77 0.01 0.01 0.04 0.03 -0.04 0.03 0.01 0.03
EXCITE38 0.00 -0.11 0.06 0.04 -0.08 -0.03 0.06 0.75 0.04 0.02 0.01 0.04 -0.02 -0.03 0.07 0.05
ATT40 0.05 0.28 -0.19 -0.08 0.05 0.12 0.04 0.11 -0.04 -0.17 0.02 0.23 0.09 -0.13 -0.02 0.02
ATT42 0.02 0.12 -0.10 -0.05 -0.03 0.13 0.04 0.15 0.09 -0.07 0.06 0.23 0.02 0.10 0.16 -0.01
PLAY43 -0.30 0.02 0.53 0.02 -0.23 -0.03 0.02 0.07 -0.08 -0.02 0.12 -0.01 -0.05 0.10 0.06 -0.11
PLAY44 -0.03 0.00 0.81 -0.03 -0.03 -0.02 -0.03 0.05 0.07 0.01 0.02 0.09 0.05 0.06 -0.11 0.00
PLAY45 -0.01 0.00 0.82 -0.07 0.07 -0.05 -0.05 0.01 -0.06 -0.06 0.07 0.02 0.01 0.10 0.01 -0.04
PLAY46 0.01 -0.12 0.81 0.01 0.07 0.03 0.00 0.02 -0.02 0.06 -0.07 -0.04 -0.06 0.02 0.01 0.11
IMP47 0.06 -0.07 0.17 -0.04 0.00 -0.02 -0.01 0.14 0.00 0.17 0.03 0.56 0.06 0.01 0.07 0.11
IMP48 -0.03 0.02 0.11 0.14 0.04 0.05 0.01 0.11 -0.01 0.08 0.02 0.61 0.05 -0.03 0.07 -0.12
MISC51 -0.02 0.06 -0.13 -0.06 -0.05 0.19 -0.02 0.04 0.11 0.10 -0.07 0.20 -0.05 0.06 0.18 0.38
MISC52 -0.06 0.05 -0.08 0.01 0.15 -0.07 0.00 0.06 -0.09 0.00 0.11 0.02 0.09 -0.02 0.72 -0.03
MISC53 -0.10 -0.06 -0.09 0.15 0.00 0.03 -0.05 0.01 -0.06 0.10 0.04 0.16 0.05 0.00 0.55 0.05
MISC54 0.00 0.14 -0.06 -0.05 -0.02 -0.04 0.66 0.07 0.00 0.01 0.01 0.01 0.14 -0.09 0.06 0.03
MISC55 0.01 -0.07 0.00 -0.07 0.02 0.03 0.87 0.00 0.07 0.02 -0.01 -0.04 -0.02 0.01 0.00 -0.04
MISC56 -0.09 -0.02 -0.09 0.14 0.02 -0.04 0.78 -0.04 -0.09 0.02 0.07 0.05 0.02 0.08 -0.05 0.05
MISC57 0.00 0.09 0.03 0.12 -0.09 0.13 -0.01 0.08 0.06 0.20 0.01 0.09 -0.05 0.25 0.16 0.10
MISC58 0.01 0.05 0.11 0.34 -0.02 0.24 0.06 -0.10 0.03 0.05 0.00 0.03 -0.15 0.14 0.09 0.08
MISC59 0.09 0.11 0.09 0.02 -0.10 0.30 0.03 -0.02 0.06 -0.04 -0.09 0.42 0.03 0.31 0.03 0.02
MISC60 0.00 0.06 0.10 -0.01 -0.03 0.01 0.07 0.12 -0.09 0.01 0.01 0.04 0.03 0.67 0.01 -0.03
MISC61 0.07 0.02 0.19 0.00 0.02 0.11 -0.02 0.15 0.05 -0.03 -0.11 -0.01 -0.05 0.67 -0.04 -0.01
MISC62 -0.08 0.39 -0.07 -0.04 0.05 -0.05 0.00 0.04 0.23 0.04 0.28 0.08 0.01 0.21 0.01 0.01
MISC64 -0.14 0.78 -0.03 0.06 0.06 0.03 -0.01 -0.02 -0.05 0.01 0.03 -0.07 0.02 0.04 -0.01 0.08
MISC65 -0.09 0.71 -0.05 -0.03 0.01 0.02 -0.02 -0.04 0.08 0.06 0.06 0.04 0.03 0.04 0.09 0.07
MISC66 0.21 0.61 -0.06 -0.01 0.01 0.04 0.14 -0.06 -0.06 0.05 -0.03 0.11 0.06 -0.04 0.00 -0.09
MISC67 0.20 0.58 -0.10 0.04 0.02 0.06 0.12 -0.05 0.02 -0.02 -0.02 0.06 0.02 0.01 0.03 -0.16
MISC69 0.06 0.09 -0.03 0.02 -0.04 0.09 0.23 0.06 0.03 -0.05 0.11 0.13 -0.20 0.00 0.07 0.25
MISC70 0.01 -0.01 0.01 -0.01 0.17 0.13 0.10 -0.02 0.16 -0.03 -0.04 0.27 -0.06 0.17 0.26 -0.02
MISC71 0.02 0.20 0.02 -0.07 0.01 0.12 0.18 -0.05 -0.08 -0.10 0.04 0.18 -0.05 0.09 0.20 0.10
2.6.6.4.1 16 Factor Model Largest Loading Per Item
Largest Loading Per Item and Associated Factors, Sorted by Factor
largest maximum itemNames itemDescriptions
13 PA1 0.28 ATT40 Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
43 PA1 0.39 MISC62 Becomes highly excited and/or distracted when encountering unfamiliar dogs
44 PA1 0.78 MISC64 When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
45 PA1 0.71 MISC65 Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
46 PA1 0.61 MISC66 Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
47 PA1 0.58 MISC67 Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
64 PA1 0.62 TRAIN07 Unfocused; is easily distracted by interesting sights, sounds or smells
65 PA1 0.10 TRAIN08 Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
24 PA10 0.42 FEAR26 When examined/treated by a veterinarian
27 PA10 0.76 FEAR29 When having nails trimmed, or feet touched/handled
28 PA10 0.65 FEAR30 When groomed or bathed
35 PA11 0.66 MISC54 Reluctant to/nervous about crossing grates or other unfamiliar surfaces
36 PA11 0.87 MISC55 Reluctant to/nervous about crossing shiny or slippery floors
37 PA11 0.78 MISC56 Nervous or frightened when ascending or descending some types of stairs
19 PA12 0.82 FEAR21 When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
20 PA12 0.39 FEAR22 In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
21 PA12 0.76 FEAR23 When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
22 PA12 0.81 FEAR24 When an unfamiliar person tries to touch or pet the dog
23 PA12 0.41 FEAR25 In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
26 PA12 0.49 FEAR28 When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
38 PA13 0.25 MISC57 Pulls excessively hard when on leash
41 PA13 0.67 MISC60 Playful, puppyish, boisterous
42 PA13 0.67 MISC61 Active, energetic, always on the go
25 PA14 0.82 FEAR27 When approached directly by an unfamiliar dog
29 PA14 0.74 FEAR31 When barked, growled, or lunged at by an unfamiliar dog
58 PA15 0.47 TRAIN01 Is hard to recall when off the leash
59 PA15 0.66 TRAIN02 Is slow to obey a ‘sit’ command
60 PA15 0.69 TRAIN03 Is slow to obey a ‘stay’ command
61 PA15 0.56 TRAIN04 Has difficulty attending/listening to things you say or do
62 PA15 0.38 TRAIN05 Is slow to respond to corrections or reprimands: thick-skinned
63 PA15 0.38 TRAIN06 Is slow to learn new tricks or tasks
14 PA16 0.23 ATT42 Becomes agitated (whines, jumps up, tries to intervene) when attention is given to another person or animal
30 PA16 0.56 IMP47 Impulsive; doesn’t seem to think before s/he acts
31 PA16 0.61 IMP48 Becomes frustrated/impatient in a wide range of situations
40 PA16 0.42 MISC59 Hyperactive, restless, has trouble settling down
49 PA16 0.27 MISC70 Barks persistently when alarmed or excited
51 PA2 0.53 PLAY43 Eagerly engages in play with new/unfamiliar people
52 PA2 0.81 PLAY44 Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
53 PA2 0.82 PLAY45 Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
54 PA2 0.81 PLAY46 Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1 PA3 0.68 AGG09 Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2 PA3 0.80 AGG10 Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6 PA3 0.63 AGG14 When strangers walk past when the dog is in his/her home run or kennel
7 PA3 0.69 AGG15 When an unfamiliar person tries to touch or pet the dog
9 PA4 0.46 AGG17 When stared at directly by you or another familiar person
32 PA4 0.38 MISC51 Escapes or would escape from home, yard or kennel given the chance
48 PA4 0.25 MISC69 Chases/follows shadows, light spots, etc.
3 PA5 0.74 AGG11 Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4 PA5 0.91 AGG12 When you or another familiar person approaches the dog directly while s/he is eating
5 PA5 0.92 AGG13 When his/her food is taken away by you or another familiar person
39 PA5 0.34 MISC58 Urinates against objects/furnishings indoors
8 PA6 0.59 AGG16 When approached directly by an unfamiliar dog while being walked/exercised on a leash
10 PA6 0.60 AGG18 When barked, growled, or lunged at by another dog
11 PA6 0.77 AGG19 Towards other familiar dogs
12 PA6 0.60 AGG20 When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
33 PA7 0.72 MISC52 Begs persistently for food when people are eating
34 PA7 0.55 MISC53 Steals food
50 PA7 0.20 MISC71 Licks people or objects excessively
55 PA8 0.79 SEPR32 Restlessness/agitation/pacing when left alone
56 PA8 0.76 SEPR33 Barking or whining when left alone
57 PA8 0.80 SEPR34 Chewing/scratching at doors, floor, fencing, etc., when left alone
15 PA9 0.62 EXCITE35 Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
16 PA9 0.71 EXCITE36 Excitable when playing with you or other familiar persons
17 PA9 0.77 EXCITE37 Excitable just before being taken out for a walk
18 PA9 0.75 EXCITE38 Excitable just before being taken out for work or training

2.6.7 16 Model Reliability Measures

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

The overall alpha for all items is 0.8814955.

The overall omega for all items is 0.930894.

Hierarchical omega is 0.6054187.

2.7 17 Factors

2.7.1 Imputation of Missing Items (17 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.7.2 17-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.7.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.6272065^{4} with 2278 DF, p = 0e+00.

2.7.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8547232

2.7.3 17-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.7.3.1 Bartlett’s Test of Sphericity

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.0608085^{4} with 2278 DF, p = 0e+00.

2.7.3.2 17-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8547232

2.7.4 Between-Item Correlations

2.7.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.717562. The maximum correlation in this data set is 0.8902964.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.6902379. The maximum correlation was 0.8890639.

2.7.5 Estimating Number of Factors

2.7.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

The suggested number of factors is 15.

2.7.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
Number of Factors MAP value
1 0.0250
2 0.0213
3 0.0163
4 0.0147
5 0.0139
6 0.0130
7 0.0125
8 0.0122
9 0.0120
10 0.0118
11 0.0115
12 0.0110
13 0.0112
14 0.0116
15 0.0117
16 0.0122
17 0.0123
18 0.0126

2.7.6 Factor Analysis for 17 Factors

2.7.6.1 17 Factors Model Fit

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

  • chi-square: 1.8817288^{4}
  • degrees of freedom: 1258
  • P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.4489462. Should be > 0.9; need reference)

2.7.6.2 17 Factor Model Communalities

fanal17.communality
TRAIN01 0.55
TRAIN02 0.43
TRAIN03 0.54
TRAIN04 0.63
TRAIN05 0.34
TRAIN06 0.36
TRAIN07 0.61
TRAIN08 0.63
AGG09 0.79
AGG10 0.73
AGG11 0.86
AGG12 0.90
AGG13 0.95
AGG14 0.51
AGG15 0.80
AGG16 0.76
AGG17 0.77
AGG18 0.73
AGG19 0.72
AGG20 0.60
FEAR21 0.83
FEAR22 0.44
FEAR23 0.80
FEAR24 0.87
FEAR25 0.50
FEAR26 0.44
FEAR27 0.84
FEAR28 0.67
FEAR29 0.61
FEAR30 0.59
FEAR31 0.69
SEPR32 0.67
SEPR33 0.65
SEPR34 0.73
EXCITE35 0.50
EXCITE36 0.62
EXCITE37 0.59
EXCITE38 0.64
ATT39 0.64
ATT40 0.49
ATT42 0.29
PLAY43 0.58
PLAY44 0.81
PLAY45 0.78
PLAY46 0.77
IMP47 0.49
IMP48 0.53
MISC50 0.40
MISC51 0.46
MISC52 0.65
MISC53 0.50
MISC54 0.62
MISC55 0.74
MISC56 0.61
MISC57 0.36
MISC58 0.28
MISC59 0.59
MISC60 0.57
MISC61 0.70
MISC62 0.53
MISC63 0.43
MISC64 0.61
MISC65 0.63
MISC66 0.69
MISC67 0.61
MISC69 0.25
MISC70 0.37
MISC71 0.28

2.7.6.3 How many communalities < 0.40?

There are 9 items with communality < 0.40.

fanal17.communality item
TRAIN05 0.34 TRAIN05
TRAIN06 0.36 TRAIN06
ATT42 0.29 ATT42
MISC50 0.40 MISC50
MISC57 0.36 MISC57
MISC58 0.28 MISC58
MISC69 0.25 MISC69
MISC70 0.37 MISC70
MISC71 0.28 MISC71

2.7.6.4 17 Factor Model Loadings

PA12 PA2 PA1 PA4 PA3 PA5 PA8 PA7 PA9 PA6 PA15 PA17 PA10 PA13 PA11 PA16 PA14
TRAIN01 -0.02 -0.08 0.18 -0.09 -0.04 -0.10 -0.05 -0.04 0.45 0.08 -0.04 0.00 0.09 0.06 0.14 -0.13 0.32
TRAIN02 0.00 0.03 0.00 0.01 0.08 0.08 0.05 0.05 0.64 -0.06 0.04 -0.08 0.06 -0.01 0.04 -0.01 -0.11
TRAIN03 0.00 -0.02 -0.04 -0.06 -0.01 0.07 0.08 0.04 0.69 0.08 -0.07 -0.01 0.04 0.04 0.07 0.03 -0.05
TRAIN04 0.07 -0.02 0.25 0.05 -0.04 -0.03 0.01 0.02 0.59 -0.06 0.03 0.15 -0.03 -0.06 -0.04 -0.11 0.08
TRAIN05 -0.09 0.05 0.10 0.16 0.09 -0.03 -0.03 0.07 0.40 0.05 -0.07 0.14 -0.11 0.01 0.03 -0.06 0.08
TRAIN06 -0.09 -0.06 0.08 0.04 -0.04 0.14 0.07 -0.05 0.44 -0.06 0.10 0.10 -0.01 -0.18 -0.14 0.09 -0.07
TRAIN07 0.07 -0.10 0.59 0.01 -0.11 -0.07 0.03 -0.01 0.27 0.02 0.01 -0.01 0.02 -0.03 -0.01 0.01 0.02
TRAIN08 0.01 -0.69 0.09 0.03 -0.03 0.07 0.02 0.04 0.08 -0.10 0.06 -0.11 0.02 0.02 0.08 0.01 0.05
AGG09 0.22 0.01 0.01 0.10 0.67 0.07 -0.10 -0.07 0.06 0.03 -0.01 0.13 0.03 0.05 -0.12 0.14 0.11
AGG10 -0.04 0.08 -0.02 0.08 0.80 -0.03 0.13 -0.01 -0.01 0.07 0.01 -0.04 0.03 -0.05 0.04 0.01 -0.04
AGG11 0.04 -0.06 -0.13 0.74 -0.10 0.01 0.03 -0.14 0.07 0.15 0.00 -0.01 0.07 0.12 0.10 0.05 0.27
AGG12 0.02 -0.06 0.04 0.92 0.05 0.03 0.04 0.07 -0.02 0.01 0.04 0.03 -0.06 -0.07 -0.04 -0.03 -0.15
AGG13 0.01 0.01 0.06 0.89 0.10 -0.01 -0.07 0.06 -0.02 0.03 -0.01 0.00 0.10 0.00 0.04 -0.05 0.03
AGG14 0.08 0.02 0.06 -0.07 0.60 0.01 0.12 0.05 -0.07 0.11 -0.01 0.05 -0.08 -0.12 0.17 0.03 0.05
AGG15 0.29 -0.05 0.00 0.10 0.70 0.02 -0.04 -0.04 0.01 0.10 -0.09 -0.06 0.07 0.09 0.03 -0.07 0.03
AGG16 -0.08 -0.04 0.04 -0.02 0.27 0.07 -0.07 -0.02 0.09 0.61 0.28 -0.01 -0.06 -0.01 -0.09 0.09 -0.01
AGG17 0.08 0.19 0.14 0.15 0.28 0.10 0.16 0.16 -0.09 0.04 0.01 -0.14 0.15 -0.25 -0.14 -0.04 0.47
AGG18 -0.12 0.00 0.01 -0.04 0.28 0.00 -0.04 -0.05 0.04 0.61 0.26 0.06 0.00 0.03 -0.07 0.08 0.04
AGG19 0.03 0.05 0.02 0.10 0.00 0.01 0.03 0.10 -0.02 0.77 0.00 -0.05 0.06 0.03 -0.05 -0.05 0.04
AGG20 0.02 0.04 -0.03 0.27 -0.12 -0.01 0.05 -0.01 -0.04 0.63 -0.09 0.09 0.09 -0.14 0.10 -0.01 -0.05
FEAR21 0.82 -0.01 -0.03 0.04 0.06 0.01 -0.01 0.00 0.01 -0.01 0.09 0.01 0.07 0.01 -0.04 0.06 0.07
FEAR22 0.38 0.00 0.19 -0.07 -0.22 0.23 0.07 0.04 -0.02 0.22 -0.09 -0.07 0.02 -0.11 0.14 -0.04 -0.16
FEAR23 0.75 -0.04 0.01 0.00 0.18 0.04 0.05 0.01 -0.02 -0.02 0.16 0.03 -0.04 0.02 -0.06 -0.01 -0.03
FEAR24 0.81 -0.08 -0.02 0.06 0.11 -0.03 -0.03 0.02 -0.01 -0.03 0.15 -0.02 0.03 0.02 -0.01 0.09 0.00
FEAR25 0.40 0.09 0.25 0.06 -0.15 0.28 0.02 0.03 0.03 0.09 0.03 0.06 -0.05 -0.11 0.11 -0.02 0.02
FEAR26 0.35 0.06 -0.02 0.06 0.01 -0.02 0.05 -0.03 0.03 0.04 0.08 -0.04 0.40 0.03 0.07 0.06 -0.03
FEAR27 0.17 0.02 0.00 0.04 -0.03 0.01 0.02 0.00 -0.02 0.07 0.84 -0.01 0.02 -0.02 0.04 -0.02 0.02
FEAR28 0.49 0.06 0.14 0.00 -0.07 0.35 0.04 0.06 0.01 0.00 0.04 0.00 0.17 -0.07 -0.05 -0.02 -0.06
FEAR29 -0.05 -0.06 -0.03 -0.03 0.03 -0.01 0.00 0.01 0.03 -0.02 0.03 -0.01 0.79 0.04 0.01 0.01 0.03
FEAR30 -0.01 0.02 0.03 0.06 -0.04 0.10 0.10 -0.02 -0.03 0.05 0.03 0.05 0.66 -0.05 0.04 -0.04 -0.05
FEAR31 0.11 0.00 0.01 -0.01 -0.11 0.05 0.05 0.00 0.00 0.01 0.74 0.00 0.10 -0.05 0.06 0.00 -0.02
SEPR32 0.07 -0.04 -0.01 -0.03 0.02 -0.05 0.77 0.07 -0.01 0.05 0.00 0.02 0.07 0.00 -0.09 0.09 -0.04
SEPR33 -0.08 -0.02 0.05 0.07 0.03 0.00 0.77 0.01 0.08 -0.03 0.04 -0.04 0.04 0.05 0.01 0.01 -0.15
SEPR34 -0.03 -0.02 0.01 -0.06 0.03 0.05 0.78 -0.02 0.01 -0.04 0.02 0.05 0.01 0.03 0.04 -0.04 0.21
EXCITE35 0.12 -0.12 0.01 -0.09 0.00 -0.09 0.15 0.61 0.05 0.05 0.00 -0.05 -0.03 0.12 0.05 0.10 -0.03
EXCITE36 -0.02 0.14 0.03 0.03 0.02 0.01 -0.05 0.70 0.01 -0.03 -0.08 0.00 0.08 0.08 -0.07 0.04 -0.04
EXCITE37 -0.03 -0.07 -0.04 0.05 -0.01 -0.02 0.03 0.76 0.03 0.01 0.04 0.00 -0.04 0.02 0.01 0.04 0.04
EXCITE38 -0.01 0.04 -0.10 0.04 -0.06 0.06 -0.04 0.77 0.00 0.03 0.02 0.05 -0.01 -0.03 0.05 -0.02 0.05
ATT39 0.05 0.08 0.00 -0.05 -0.01 -0.03 0.03 0.08 -0.02 0.03 -0.05 -0.08 -0.03 0.08 0.11 0.75 -0.02
ATT40 0.02 -0.11 0.21 -0.01 -0.02 0.05 0.05 0.04 -0.04 -0.02 -0.02 0.27 0.10 -0.19 -0.02 0.47 0.09
ATT42 0.01 -0.08 0.10 -0.03 -0.04 0.04 0.11 0.14 -0.04 0.09 0.05 0.24 0.02 0.11 0.16 0.12 -0.01
PLAY43 -0.30 0.51 0.04 0.01 -0.22 0.02 -0.02 0.08 -0.06 -0.09 0.12 0.00 -0.04 0.09 0.04 -0.06 -0.12
PLAY44 -0.04 0.84 0.00 -0.02 -0.05 -0.02 -0.03 0.04 0.03 0.07 0.02 0.08 0.05 0.05 -0.11 0.05 0.01
PLAY45 0.00 0.84 0.01 -0.06 0.05 -0.04 -0.05 0.00 -0.05 -0.06 0.07 0.00 0.00 0.08 0.02 0.04 -0.03
PLAY46 0.02 0.82 -0.09 -0.01 0.06 0.01 0.04 0.03 0.04 0.00 -0.07 -0.08 -0.07 0.01 0.04 -0.05 0.10
IMP47 0.05 0.20 -0.07 -0.04 0.05 -0.05 0.00 0.16 0.23 0.01 0.05 0.44 0.09 0.04 0.12 -0.08 0.03
IMP48 -0.02 0.15 0.00 0.14 0.07 -0.02 0.07 0.13 0.16 0.01 0.03 0.47 0.09 0.00 0.13 -0.05 -0.18
MISC50 -0.03 0.01 -0.03 0.24 -0.08 0.07 0.19 0.08 0.06 -0.07 0.06 0.35 -0.05 0.05 -0.08 0.09 0.23
MISC51 -0.03 -0.14 0.07 -0.08 -0.02 -0.04 0.19 0.07 0.09 0.10 -0.05 0.23 -0.03 0.08 0.17 -0.13 0.36
MISC52 -0.03 -0.04 0.05 0.01 0.10 0.03 -0.05 0.03 0.00 -0.07 0.08 -0.03 0.05 -0.04 0.77 0.09 -0.03
MISC53 -0.08 -0.06 -0.06 0.14 -0.02 -0.04 0.03 0.00 0.10 -0.04 0.03 0.13 0.03 -0.01 0.58 0.01 0.03
MISC54 0.01 -0.05 0.12 -0.04 -0.03 0.66 -0.04 0.06 0.03 0.00 0.01 -0.01 0.13 -0.09 0.07 0.03 0.03
MISC55 0.00 -0.02 -0.07 -0.07 0.03 0.88 0.03 0.01 0.00 0.06 -0.01 -0.01 -0.01 0.02 -0.02 -0.04 -0.03
MISC56 -0.08 -0.05 -0.02 0.15 0.02 0.76 -0.04 -0.05 0.06 -0.08 0.06 0.00 0.02 0.08 -0.01 0.04 0.05
MISC57 0.00 0.03 0.13 0.09 -0.07 -0.02 0.14 0.10 0.17 0.06 0.00 0.07 -0.04 0.26 0.18 -0.09 0.06
MISC58 0.03 0.14 0.04 0.33 -0.04 0.07 0.24 -0.12 0.08 0.05 -0.01 0.01 -0.16 0.12 0.12 0.02 0.09
MISC59 0.09 0.12 0.09 0.01 -0.07 0.00 0.31 -0.01 0.02 0.05 -0.08 0.40 0.06 0.30 0.03 -0.03 -0.01
MISC60 0.00 0.11 0.05 0.00 -0.03 0.06 0.03 0.11 0.01 -0.10 -0.01 0.04 0.04 0.66 -0.01 0.06 -0.03
MISC61 0.07 0.20 0.02 0.00 0.01 -0.02 0.13 0.14 -0.05 0.04 -0.12 0.00 -0.05 0.65 -0.06 0.04 0.00
MISC62 -0.10 -0.08 0.44 -0.04 0.08 -0.01 -0.07 0.05 0.01 0.22 0.29 0.07 0.03 0.24 0.02 -0.01 -0.02
MISC63 -0.05 -0.08 0.42 0.02 0.09 0.07 -0.12 0.18 -0.06 -0.01 0.11 0.21 0.05 0.18 0.09 -0.09 -0.03
MISC64 -0.12 -0.03 0.75 0.07 0.04 0.00 0.06 -0.05 0.04 -0.04 0.01 -0.09 0.02 0.03 0.01 0.05 0.09
MISC65 -0.07 -0.05 0.68 -0.03 0.00 -0.01 0.04 -0.06 0.08 0.08 0.06 0.04 0.04 0.02 0.09 0.02 0.07
MISC66 0.22 -0.07 0.58 -0.01 0.01 0.15 0.06 -0.06 0.08 -0.06 -0.02 0.11 0.06 -0.05 -0.01 0.02 -0.10
MISC67 0.21 -0.10 0.53 0.06 -0.01 0.14 0.07 -0.08 0.02 0.02 -0.02 0.08 0.02 -0.02 0.00 0.09 -0.13
MISC69 0.05 -0.03 0.07 0.01 -0.04 0.23 0.08 0.06 -0.02 0.02 0.11 0.18 -0.18 0.00 0.05 0.02 0.26
MISC70 0.00 -0.03 -0.01 -0.02 0.19 0.09 0.14 0.01 -0.06 0.14 -0.02 0.35 -0.03 0.17 0.20 -0.08 -0.03
MISC71 0.01 0.01 0.17 -0.06 0.00 0.18 0.09 -0.05 -0.10 -0.10 0.05 0.27 -0.02 0.09 0.16 0.05 0.12
2.7.6.4.1 17 Factor Model Largest Loading Per Item
Largest Loading Per Item and Associated Factors, Sorted by Factor
largest maximum itemNames itemDescriptions
45 PA1 0.44 MISC62 Becomes highly excited and/or distracted when encountering unfamiliar dogs
46 PA1 0.42 MISC63 Becomes highly excited and/or distracted when encountering unfamiliar people
47 PA1 0.75 MISC64 When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
48 PA1 0.68 MISC65 Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
49 PA1 0.58 MISC66 Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
50 PA1 0.53 MISC67 Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
67 PA1 0.59 TRAIN07 Unfocused; is easily distracted by interesting sights, sounds or smells
68 PA1 0.09 TRAIN08 Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
25 PA10 0.40 FEAR26 When examined/treated by a veterinarian
28 PA10 0.79 FEAR29 When having nails trimmed, or feet touched/handled
29 PA10 0.66 FEAR30 When groomed or bathed
35 PA11 0.77 MISC52 Begs persistently for food when people are eating
36 PA11 0.58 MISC53 Steals food
20 PA12 0.82 FEAR21 When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
21 PA12 0.38 FEAR22 In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
22 PA12 0.75 FEAR23 When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
23 PA12 0.81 FEAR24 When an unfamiliar person tries to touch or pet the dog
24 PA12 0.40 FEAR25 In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
27 PA12 0.49 FEAR28 When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
40 PA13 0.26 MISC57 Pulls excessively hard when on leash
43 PA13 0.66 MISC60 Playful, puppyish, boisterous
44 PA13 0.65 MISC61 Active, energetic, always on the go
9 PA14 0.47 AGG17 When stared at directly by you or another familiar person
34 PA14 0.36 MISC51 Escapes or would escape from home, yard or kennel given the chance
51 PA14 0.26 MISC69 Chases/follows shadows, light spots, etc.
26 PA15 0.84 FEAR27 When approached directly by an unfamiliar dog
30 PA15 0.74 FEAR31 When barked, growled, or lunged at by an unfamiliar dog
13 PA16 0.75 ATT39 Displays a strong attachment for you or another familiar person
14 PA16 0.47 ATT40 Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
15 PA17 0.24 ATT42 Becomes agitated (whines, jumps up, tries to intervene) when attention is given to another person or animal
31 PA17 0.44 IMP47 Impulsive; doesn’t seem to think before s/he acts
32 PA17 0.47 IMP48 Becomes frustrated/impatient in a wide range of situations
33 PA17 0.35 MISC50 NA
42 PA17 0.40 MISC59 Hyperactive, restless, has trouble settling down
52 PA17 0.35 MISC70 Barks persistently when alarmed or excited
53 PA17 0.27 MISC71 Licks people or objects excessively
54 PA2 0.51 PLAY43 Eagerly engages in play with new/unfamiliar people
55 PA2 0.84 PLAY44 Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
56 PA2 0.84 PLAY45 Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
57 PA2 0.82 PLAY46 Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1 PA3 0.67 AGG09 Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2 PA3 0.80 AGG10 Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6 PA3 0.60 AGG14 When strangers walk past when the dog is in his/her home run or kennel
7 PA3 0.70 AGG15 When an unfamiliar person tries to touch or pet the dog
3 PA4 0.74 AGG11 Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4 PA4 0.92 AGG12 When you or another familiar person approaches the dog directly while s/he is eating
5 PA4 0.89 AGG13 When his/her food is taken away by you or another familiar person
41 PA4 0.33 MISC58 Urinates against objects/furnishings indoors
37 PA5 0.66 MISC54 Reluctant to/nervous about crossing grates or other unfamiliar surfaces
38 PA5 0.88 MISC55 Reluctant to/nervous about crossing shiny or slippery floors
39 PA5 0.76 MISC56 Nervous or frightened when ascending or descending some types of stairs
8 PA6 0.61 AGG16 When approached directly by an unfamiliar dog while being walked/exercised on a leash
10 PA6 0.61 AGG18 When barked, growled, or lunged at by another dog
11 PA6 0.77 AGG19 Towards other familiar dogs
12 PA6 0.63 AGG20 When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
16 PA7 0.61 EXCITE35 Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
17 PA7 0.70 EXCITE36 Excitable when playing with you or other familiar persons
18 PA7 0.76 EXCITE37 Excitable just before being taken out for a walk
19 PA7 0.77 EXCITE38 Excitable just before being taken out for work or training
58 PA8 0.77 SEPR32 Restlessness/agitation/pacing when left alone
59 PA8 0.77 SEPR33 Barking or whining when left alone
60 PA8 0.78 SEPR34 Chewing/scratching at doors, floor, fencing, etc., when left alone
61 PA9 0.45 TRAIN01 Is hard to recall when off the leash
62 PA9 0.64 TRAIN02 Is slow to obey a ‘sit’ command
63 PA9 0.69 TRAIN03 Is slow to obey a ‘stay’ command
64 PA9 0.59 TRAIN04 Has difficulty attending/listening to things you say or do
65 PA9 0.40 TRAIN05 Is slow to respond to corrections or reprimands: thick-skinned
66 PA9 0.44 TRAIN06 Is slow to learn new tricks or tasks

2.7.7 17 Model Reliability Measures

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

The overall alpha for all items is 0.8852365.

The overall omega for all items is 0.9332413.

Hierarchical omega is 0.6061739.

2.8 18 Factors

2.8.1 Imputation of Missing Items (18 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.8.2 18-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.8.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.7421286^{4} with 2346 DF, p = 0e+00.

2.8.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8539612

2.8.3 18-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.8.3.1 Bartlett’s Test of Sphericity

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.1657862^{4} with 2346 DF, p = 0e+00.

2.8.3.2 18-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8539612

2.8.4 Between-Item Correlations

2.8.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.7175677. The maximum correlation in this data set is 0.8898946.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.6902114. The maximum correlation was 0.8877677.

2.8.5 Estimating Number of Factors

2.8.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

The suggested number of factors is 15.

2.8.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
Number of Factors MAP value
1 0.0246
2 0.0209
3 0.0161
4 0.0145
5 0.0138
6 0.0129
7 0.0125
8 0.0122
9 0.0122
10 0.0118
11 0.0117
12 0.0113
13 0.0112
14 0.0115
15 0.0117
16 0.0120
17 0.0124
18 0.0124

2.8.6 Factor Analysis for 18 Factors

2.8.6.1 18 Factors Model Fit

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

  • chi-square: 1.9000958^{4}
  • degrees of freedom: 1257
  • P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.4352052. Should be > 0.9; need reference)

2.8.6.2 18 Factor Model Communalities

fanal18.communality
TRAIN01 0.56
TRAIN02 0.43
TRAIN03 0.53
TRAIN04 0.64
TRAIN05 0.34
TRAIN06 0.36
TRAIN07 0.63
TRAIN08 0.63
AGG09 0.80
AGG10 0.73
AGG11 0.86
AGG12 0.89
AGG13 0.97
AGG14 0.52
AGG15 0.79
AGG16 0.76
AGG17 0.80
AGG18 0.73
AGG19 0.72
AGG20 0.60
FEAR21 0.83
FEAR22 0.43
FEAR23 0.80
FEAR24 0.87
FEAR25 0.52
FEAR26 0.44
FEAR27 0.83
FEAR28 0.67
FEAR29 0.64
FEAR30 0.58
FEAR31 0.71
SEPR32 0.67
SEPR33 0.67
SEPR34 0.73
EXCITE35 0.50
EXCITE36 0.62
EXCITE37 0.61
EXCITE38 0.64
ATT39 0.65
ATT40 0.49
ATT42 0.32
PLAY43 0.58
PLAY44 0.81
PLAY45 0.78
PLAY46 0.77
IMP47 0.49
IMP48 0.52
MISC50 0.38
MISC51 0.46
MISC52 0.63
MISC53 0.51
MISC54 0.62
MISC55 0.76
MISC56 0.64
MISC57 0.36
MISC58 0.36
MISC59 0.62
MISC60 0.58
MISC61 0.69
MISC62 0.53
MISC63 0.43
MISC64 0.61
MISC65 0.63
MISC66 0.69
MISC67 0.64
MISC68 0.68
MISC69 0.39
MISC70 0.37
MISC71 0.30

2.8.6.3 How many communalities < 0.40?

There are 9 items with communality < 0.40.

fanal18.communality item
TRAIN05 0.34 TRAIN05
TRAIN06 0.36 TRAIN06
ATT42 0.32 ATT42
MISC50 0.38 MISC50
MISC57 0.36 MISC57
MISC58 0.36 MISC58
MISC69 0.39 MISC69
MISC70 0.37 MISC70
MISC71 0.30 MISC71

2.8.6.4 18 Factor Model Loadings

PA16 PA2 PA1 PA4 PA3 PA6 PA5 PA10 PA11 PA8 PA12 PA18 PA9 PA14 PA7 PA13 PA15 PA17
TRAIN01 -0.03 -0.09 0.16 -0.11 -0.04 -0.06 -0.10 -0.03 0.46 0.07 -0.03 0.03 0.08 0.06 0.15 0.01 -0.13 0.31
TRAIN02 0.01 0.04 0.00 0.02 0.08 0.06 0.09 0.05 0.64 -0.06 0.04 -0.09 0.06 -0.01 0.03 -0.05 -0.01 -0.09
TRAIN03 0.00 -0.02 -0.04 -0.05 -0.02 0.08 0.08 0.05 0.69 0.08 -0.07 -0.01 0.04 0.04 0.06 -0.05 0.03 -0.03
TRAIN04 0.08 -0.02 0.23 0.04 -0.04 0.00 -0.05 0.01 0.60 -0.05 0.02 0.12 -0.02 -0.06 -0.04 0.14 -0.10 0.02
TRAIN05 -0.07 0.04 0.08 0.15 0.10 -0.03 -0.06 0.05 0.41 0.06 -0.09 0.12 -0.09 0.01 0.04 0.12 -0.05 0.01
TRAIN06 -0.09 -0.06 0.07 0.04 -0.04 0.07 0.15 -0.04 0.44 -0.07 0.11 0.11 -0.02 -0.18 -0.15 -0.02 0.08 -0.05
TRAIN07 0.08 -0.10 0.58 0.00 -0.11 0.03 -0.08 -0.03 0.28 0.03 -0.01 -0.04 0.04 -0.03 -0.01 0.12 0.02 -0.02
TRAIN08 0.00 -0.69 0.09 0.03 -0.03 0.02 0.07 0.04 0.07 -0.10 0.06 -0.10 0.02 0.02 0.08 -0.01 0.01 0.06
AGG09 0.21 0.01 0.01 0.09 0.66 -0.10 0.06 -0.07 0.06 0.03 0.00 0.15 0.02 0.05 -0.12 0.01 0.14 0.12
AGG10 -0.03 0.08 -0.01 0.09 0.79 0.13 -0.03 -0.01 -0.01 0.07 0.01 -0.05 0.03 -0.05 0.03 0.00 0.01 -0.02
AGG11 0.03 -0.08 -0.14 0.71 -0.10 0.02 0.00 -0.13 0.07 0.15 0.01 0.02 0.07 0.12 0.11 0.06 0.04 0.29
AGG12 0.02 -0.06 0.05 0.91 0.05 0.05 0.03 0.08 -0.02 0.02 0.04 0.02 -0.05 -0.07 -0.04 -0.02 -0.04 -0.11
AGG13 0.03 0.00 0.05 0.89 0.10 -0.07 -0.03 0.05 -0.01 0.03 -0.02 -0.02 0.11 0.00 0.04 0.10 -0.04 0.01
AGG14 0.10 0.02 0.06 -0.08 0.60 0.12 -0.01 0.03 -0.07 0.12 -0.03 0.02 -0.06 -0.12 0.18 0.08 0.03 0.00
AGG15 0.29 -0.05 0.00 0.11 0.69 -0.03 0.03 -0.03 0.00 0.10 -0.08 -0.05 0.06 0.09 0.03 -0.03 -0.07 0.07
AGG16 -0.08 -0.03 0.04 -0.02 0.27 -0.06 0.07 -0.02 0.09 0.61 0.29 -0.01 -0.06 0.00 -0.09 -0.02 0.09 0.00
AGG17 0.07 0.17 0.13 0.12 0.27 0.14 0.08 0.17 -0.10 0.04 0.02 -0.09 0.14 -0.24 -0.13 0.07 -0.05 0.53
AGG18 -0.12 0.00 0.01 -0.04 0.27 -0.04 0.00 -0.04 0.04 0.62 0.26 0.07 0.00 0.03 -0.07 -0.01 0.07 0.04
AGG19 0.04 0.05 0.02 0.10 0.00 0.03 0.01 0.09 -0.02 0.77 0.00 -0.05 0.07 0.04 -0.05 0.04 -0.05 0.05
AGG20 0.02 0.04 -0.03 0.27 -0.12 0.05 -0.01 -0.02 -0.04 0.64 -0.09 0.08 0.10 -0.14 0.10 0.02 -0.01 -0.06
FEAR21 0.82 -0.01 -0.03 0.04 0.06 -0.01 0.01 0.00 0.02 -0.01 0.09 0.03 0.07 0.02 -0.04 -0.01 0.06 0.08
FEAR22 0.37 0.00 0.21 -0.05 -0.23 0.08 0.25 0.05 -0.02 0.21 -0.08 -0.06 0.02 -0.11 0.13 -0.10 -0.05 -0.10
FEAR23 0.76 -0.04 0.01 0.00 0.17 0.05 0.03 0.00 -0.01 -0.02 0.15 0.02 -0.03 0.02 -0.06 0.04 -0.01 -0.05
FEAR24 0.81 -0.09 -0.02 0.06 0.11 -0.03 -0.04 0.01 -0.01 -0.03 0.15 -0.02 0.03 0.02 -0.02 0.01 0.09 0.00
FEAR25 0.41 0.09 0.25 0.05 -0.15 0.01 0.25 0.02 0.03 0.10 0.02 0.04 -0.04 -0.11 0.11 0.14 -0.01 -0.02
FEAR26 0.35 0.06 -0.01 0.07 0.00 0.05 -0.01 -0.04 0.03 0.04 0.08 -0.04 0.40 0.03 0.06 -0.01 0.06 -0.01
FEAR27 0.17 0.02 0.00 0.02 -0.03 0.01 -0.01 -0.01 -0.02 0.08 0.82 -0.02 0.02 -0.02 0.04 0.07 -0.02 -0.01
FEAR28 0.48 0.06 0.15 0.01 -0.08 0.04 0.36 0.07 0.01 -0.01 0.05 0.03 0.15 -0.07 -0.05 -0.10 -0.03 0.01
FEAR29 -0.04 -0.05 -0.03 -0.03 0.03 0.01 -0.01 -0.01 0.03 -0.01 0.03 -0.02 0.80 0.04 0.02 0.03 0.02 0.01
FEAR30 -0.01 0.03 0.04 0.07 -0.04 0.11 0.11 -0.02 -0.03 0.05 0.05 0.06 0.64 -0.05 0.04 -0.05 -0.04 -0.01
FEAR31 0.10 0.00 0.01 -0.01 -0.10 0.05 0.05 0.02 0.00 0.00 0.77 0.01 0.09 -0.05 0.06 -0.03 -0.01 0.01
SEPR32 0.06 -0.04 0.00 -0.02 0.02 0.77 -0.04 0.08 -0.01 0.04 0.01 0.05 0.05 0.00 -0.10 -0.05 0.09 0.01
SEPR33 -0.07 -0.01 0.05 0.08 0.04 0.78 0.00 -0.01 0.08 -0.03 0.03 -0.06 0.05 0.04 0.01 0.01 0.02 -0.16
SEPR34 -0.03 -0.03 -0.01 -0.08 0.03 0.76 0.03 -0.02 0.01 -0.04 0.02 0.06 0.02 0.03 0.05 0.12 -0.04 0.19
EXCITE35 0.12 -0.12 0.00 -0.09 -0.01 0.15 -0.09 0.60 0.05 0.05 -0.01 -0.07 -0.02 0.12 0.04 0.05 0.10 -0.05
EXCITE36 -0.02 0.15 0.03 0.03 0.02 -0.05 0.01 0.69 0.01 -0.03 -0.08 -0.01 0.08 0.08 -0.07 0.04 0.05 -0.04
EXCITE37 -0.04 -0.07 -0.04 0.05 -0.01 0.03 -0.01 0.78 0.03 0.01 0.05 0.02 -0.05 0.03 0.01 -0.04 0.04 0.07
EXCITE38 -0.01 0.04 -0.10 0.03 -0.06 -0.04 0.05 0.78 0.00 0.03 0.02 0.05 -0.01 -0.03 0.05 0.00 -0.03 0.05
ATT39 0.05 0.08 0.00 -0.05 -0.01 0.03 -0.03 0.07 -0.02 0.03 -0.05 -0.08 -0.01 0.07 0.10 0.01 0.76 -0.03
ATT40 0.00 -0.12 0.20 -0.02 -0.02 0.05 0.04 0.05 -0.04 -0.03 -0.01 0.29 0.09 -0.19 -0.02 0.02 0.46 0.09
ATT42 0.03 -0.08 0.09 -0.05 -0.04 0.11 0.00 0.11 -0.03 0.11 0.02 0.20 0.06 0.10 0.17 0.19 0.13 -0.13
PLAY43 -0.29 0.51 0.04 0.01 -0.22 -0.02 0.02 0.07 -0.06 -0.09 0.11 -0.03 -0.04 0.09 0.04 0.06 -0.06 -0.14
PLAY44 -0.03 0.84 0.00 -0.02 -0.04 -0.03 -0.02 0.04 0.04 0.07 0.01 0.08 0.05 0.05 -0.10 0.01 0.05 0.01
PLAY45 0.00 0.85 0.01 -0.06 0.05 -0.04 -0.03 0.00 -0.05 -0.06 0.07 0.00 -0.01 0.08 0.02 -0.04 0.04 -0.01
PLAY46 0.02 0.82 -0.09 -0.02 0.06 0.04 0.00 0.03 0.04 0.00 -0.08 -0.08 -0.07 0.02 0.04 0.02 -0.05 0.11
IMP47 0.05 0.21 -0.07 -0.05 0.05 -0.01 -0.06 0.16 0.24 0.01 0.05 0.42 0.09 0.03 0.13 0.07 -0.08 -0.03
IMP48 -0.03 0.16 0.00 0.16 0.07 0.07 -0.02 0.13 0.16 0.00 0.05 0.45 0.08 -0.01 0.13 0.03 -0.05 -0.20
MISC50 -0.02 0.01 -0.04 0.20 -0.07 0.17 0.03 0.09 0.07 -0.06 0.04 0.34 -0.04 0.04 -0.05 0.15 0.08 0.16
MISC51 -0.03 -0.15 0.05 -0.11 -0.01 0.17 -0.07 0.08 0.09 0.10 -0.06 0.24 -0.03 0.08 0.19 0.14 -0.13 0.29
MISC52 -0.04 -0.05 0.05 0.01 0.10 -0.05 0.04 0.04 -0.01 -0.08 0.09 -0.03 0.06 -0.04 0.76 -0.04 0.09 -0.02
MISC53 -0.08 -0.06 -0.06 0.14 -0.02 0.03 -0.05 0.00 0.11 -0.05 0.03 0.11 0.04 -0.01 0.59 0.02 0.02 -0.01
MISC54 0.01 -0.05 0.13 -0.04 -0.03 -0.03 0.65 0.07 0.03 0.01 0.02 0.01 0.12 -0.09 0.08 -0.04 0.02 0.06
MISC55 0.03 -0.02 -0.07 -0.09 0.03 0.03 0.85 -0.01 0.00 0.07 -0.03 -0.04 0.01 0.01 -0.01 0.14 -0.04 -0.09
MISC56 -0.09 -0.06 -0.02 0.14 0.02 -0.04 0.77 -0.03 0.05 -0.09 0.08 0.03 0.01 0.08 -0.01 0.00 0.03 0.10
MISC57 0.01 0.03 0.12 0.08 -0.07 0.14 -0.02 0.10 0.18 0.06 -0.01 0.07 -0.03 0.26 0.19 0.03 -0.09 0.03
MISC58 0.00 0.14 0.04 0.33 -0.05 0.24 0.10 -0.09 0.07 0.03 0.03 0.06 -0.21 0.13 0.13 -0.16 0.01 0.22
MISC59 0.07 0.12 0.08 0.02 -0.07 0.31 0.01 0.01 0.01 0.04 -0.06 0.44 0.04 0.29 0.03 -0.05 -0.04 0.02
MISC60 0.01 0.11 0.05 -0.01 -0.03 0.03 0.06 0.10 0.01 -0.09 -0.01 0.03 0.05 0.66 -0.01 0.07 0.06 -0.07
MISC61 0.07 0.20 0.02 -0.01 0.01 0.13 -0.02 0.15 -0.05 0.04 -0.12 0.02 -0.05 0.64 -0.06 0.00 0.04 0.00
MISC62 -0.11 -0.08 0.44 -0.04 0.08 -0.06 -0.01 0.06 0.01 0.22 0.29 0.08 0.02 0.24 0.02 -0.02 -0.02 -0.02
MISC63 -0.05 -0.08 0.42 0.02 0.09 -0.12 0.06 0.18 -0.06 0.00 0.10 0.21 0.05 0.17 0.10 0.01 -0.10 -0.06
MISC64 -0.12 -0.04 0.73 0.05 0.04 0.05 -0.01 -0.06 0.05 -0.04 0.00 -0.09 0.03 0.03 0.01 0.09 0.06 0.08
MISC65 -0.07 -0.06 0.66 -0.04 0.00 0.04 -0.02 -0.06 0.08 0.08 0.06 0.04 0.04 0.02 0.09 0.05 0.02 0.07
MISC66 0.21 -0.07 0.58 0.01 0.02 0.06 0.16 -0.05 0.08 -0.07 -0.01 0.12 0.05 -0.05 -0.01 -0.02 0.01 -0.06
MISC67 0.18 -0.10 0.55 0.08 -0.01 0.08 0.16 -0.05 0.01 0.00 0.01 0.13 0.00 -0.02 0.00 -0.18 0.08 -0.03
MISC68 -0.01 0.01 0.01 0.09 0.00 0.02 0.08 -0.01 0.00 -0.01 0.02 -0.04 0.03 0.02 -0.05 0.79 0.00 -0.04
MISC69 0.10 -0.04 0.03 -0.05 -0.04 0.04 0.15 0.01 -0.02 0.05 0.06 0.11 -0.14 -0.01 0.07 0.49 0.04 0.08
MISC70 0.00 -0.02 -0.01 -0.02 0.19 0.14 0.07 0.02 -0.06 0.14 -0.02 0.34 -0.03 0.16 0.22 0.02 -0.08 -0.07
MISC71 0.01 0.00 0.16 -0.08 0.00 0.08 0.14 -0.06 -0.10 -0.10 0.04 0.26 -0.01 0.08 0.17 0.19 0.05 0.06
2.8.6.4.1 18 Factor Model Largest Loading Per Item
Largest Loading Per Item and Associated Factors, Sorted by Factor
largest maximum itemNames itemDescriptions
45 PA1 0.44 MISC62 Becomes highly excited and/or distracted when encountering unfamiliar dogs
46 PA1 0.42 MISC63 Becomes highly excited and/or distracted when encountering unfamiliar people
47 PA1 0.73 MISC64 When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
48 PA1 0.66 MISC65 Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
49 PA1 0.58 MISC66 Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
50 PA1 0.55 MISC67 Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
68 PA1 0.58 TRAIN07 Unfocused; is easily distracted by interesting sights, sounds or smells
69 PA1 0.09 TRAIN08 Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
16 PA10 0.60 EXCITE35 Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
17 PA10 0.69 EXCITE36 Excitable when playing with you or other familiar persons
18 PA10 0.78 EXCITE37 Excitable just before being taken out for a walk
19 PA10 0.78 EXCITE38 Excitable just before being taken out for work or training
62 PA11 0.46 TRAIN01 Is hard to recall when off the leash
63 PA11 0.64 TRAIN02 Is slow to obey a ‘sit’ command
64 PA11 0.69 TRAIN03 Is slow to obey a ‘stay’ command
65 PA11 0.60 TRAIN04 Has difficulty attending/listening to things you say or do
66 PA11 0.41 TRAIN05 Is slow to respond to corrections or reprimands: thick-skinned
67 PA11 0.44 TRAIN06 Is slow to learn new tricks or tasks
26 PA12 0.82 FEAR27 When approached directly by an unfamiliar dog
30 PA12 0.77 FEAR31 When barked, growled, or lunged at by an unfamiliar dog
51 PA13 0.79 MISC68 Chases own tail/hind end
52 PA13 0.49 MISC69 Chases/follows shadows, light spots, etc.
40 PA14 0.26 MISC57 Pulls excessively hard when on leash
43 PA14 0.66 MISC60 Playful, puppyish, boisterous
44 PA14 0.64 MISC61 Active, energetic, always on the go
13 PA15 0.76 ATT39 Displays a strong attachment for you or another familiar person
14 PA15 0.46 ATT40 Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
20 PA16 0.82 FEAR21 When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
21 PA16 0.37 FEAR22 In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
22 PA16 0.76 FEAR23 When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
23 PA16 0.81 FEAR24 When an unfamiliar person tries to touch or pet the dog
24 PA16 0.41 FEAR25 In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
27 PA16 0.48 FEAR28 When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
9 PA17 0.53 AGG17 When stared at directly by you or another familiar person
34 PA17 0.29 MISC51 Escapes or would escape from home, yard or kennel given the chance
15 PA18 0.20 ATT42 Becomes agitated (whines, jumps up, tries to intervene) when attention is given to another person or animal
31 PA18 0.42 IMP47 Impulsive; doesn’t seem to think before s/he acts
32 PA18 0.45 IMP48 Becomes frustrated/impatient in a wide range of situations
33 PA18 0.34 MISC50 NA
42 PA18 0.44 MISC59 Hyperactive, restless, has trouble settling down
53 PA18 0.34 MISC70 Barks persistently when alarmed or excited
54 PA18 0.26 MISC71 Licks people or objects excessively
55 PA2 0.51 PLAY43 Eagerly engages in play with new/unfamiliar people
56 PA2 0.84 PLAY44 Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
57 PA2 0.85 PLAY45 Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
58 PA2 0.82 PLAY46 Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1 PA3 0.66 AGG09 Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2 PA3 0.79 AGG10 Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6 PA3 0.60 AGG14 When strangers walk past when the dog is in his/her home run or kennel
7 PA3 0.69 AGG15 When an unfamiliar person tries to touch or pet the dog
3 PA4 0.71 AGG11 Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4 PA4 0.91 AGG12 When you or another familiar person approaches the dog directly while s/he is eating
5 PA4 0.89 AGG13 When his/her food is taken away by you or another familiar person
41 PA4 0.33 MISC58 Urinates against objects/furnishings indoors
37 PA5 0.65 MISC54 Reluctant to/nervous about crossing grates or other unfamiliar surfaces
38 PA5 0.85 MISC55 Reluctant to/nervous about crossing shiny or slippery floors
39 PA5 0.77 MISC56 Nervous or frightened when ascending or descending some types of stairs
59 PA6 0.77 SEPR32 Restlessness/agitation/pacing when left alone
60 PA6 0.78 SEPR33 Barking or whining when left alone
61 PA6 0.76 SEPR34 Chewing/scratching at doors, floor, fencing, etc., when left alone
35 PA7 0.76 MISC52 Begs persistently for food when people are eating
36 PA7 0.59 MISC53 Steals food
8 PA8 0.61 AGG16 When approached directly by an unfamiliar dog while being walked/exercised on a leash
10 PA8 0.62 AGG18 When barked, growled, or lunged at by another dog
11 PA8 0.77 AGG19 Towards other familiar dogs
12 PA8 0.64 AGG20 When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
25 PA9 0.40 FEAR26 When examined/treated by a veterinarian
28 PA9 0.80 FEAR29 When having nails trimmed, or feet touched/handled
29 PA9 0.64 FEAR30 When groomed or bathed

2.8.7 18 Model Reliability Measures

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

The overall alpha for all items is 0.8850577.

The overall omega for all items is 0.9334918.

Hierarchical omega is 0.6177792.